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diff --git a/old/slstr10.txt b/old/slstr10.txt new file mode 100644 index 0000000..50bb3a9 --- /dev/null +++ b/old/slstr10.txt @@ -0,0 +1,10317 @@ +The Project Gutenberg Etext of Side-Lights On Astronomy, by Simon Newcomb +#X in our series by Simon Newcomb + +Copyright laws are changing all over the world, be sure to check +the laws for your country before redistributing these files!!! + +Please take a look at the important information in this header. +We encourage you to keep this file on your own disk, keeping an +electronic path open for the next readers. + +Please do not remove this. + +This should be the first thing seen when anyone opens the book. +Do not change or edit it without written permission. 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THE ORGANIZATION OF SCIENTIFIC RESEARCH + XII. CAN WE MAKE IT RAIN? + XIII. THE ASTRONOMICAL EPHEMERIS AND NAUTICAL ALMANAC + XIV. THE WORLD'S DEBT TO ASTRONOMY + XV. AN ASTRONOMICAL FRIENDSHIP + XVI. THE EVOLUTION OF THE SCIENTIFIC INVESTIGATOR + XVII. THE EVOLUTION OF ASTRONOMICAL KNOWLEDGE +XVIII. ASPECTS OF AMERICAN ASTRONOMY + XIX. THE UNIVERSE AS AN ORGANISM + XX. THE RELATION OF SCIENTIFIC METHOD TO SOCIAL PROGRESS + XXI. THE OUTLOOK FOR THE FLYING-MACHINE + + + + +ILLUSTRATIONS + +SIMON NEWCOMB + +PHOTOGRAPH OP THE CORONA OP THE SUN, TAKEN IN TRIPOLI DURING TOTAL +ECLIPSE OF AUGUST 30, 1905. + +A TYPICAL STAR CLUSTER-CENTAURI + +THE GLASS DISK + +THE OPTICIAN'S TOOL + +THE OPTICIAN'S TOOL + +GRINDING A LARGE LENS + +IMAGE OF CANDLE-FLAME IN OBJECT-GLASS + +TESTING ADJUSTMENT OF OBJECT-GLASS + +A VERY PRIMITIVE MOUNTING FOR A TELESCOPE + +THE HUYGHENIAN EYE-PIECE + +SECTION OF THE PRIMITIVE MOUNTING + +SPECTRAL IMAGES OF STARS, THE UPPER LINE SHOWING HOW THEY APPEAR +WITH THE EYE-PIECE PUSHED IN, THE LOWER WITH THE EYE-PIECE DRAWN +OUT + +THE GREAT REFRACTOR OF THE NATIONAL OBSERVATORY AT WASHINGTON + +THE "BROKEN-BACKED COMET-SEEKER" + +NEBULA IN ORION + +DIP OF THE MAGNETIC NEEDLE IN VARIOUS LATITUDES + +STAR SPECTRA + +PROFESSOR LANGLEY'S AIR-SHIP + + + + + + +PREFACE + +In preparing and issuing this collection of essays and addresses, +the author has yielded to what he could not but regard as the too +flattering judgment of the publishers. Having done this, it became +incumbent to do what he could to justify their good opinion by +revising the material and bringing it up to date. Interest rather +than unity of thought has determined the selection. + +A prominent theme in the collection is that of the structure, +extent, and duration of the universe. Here some repetition of +ideas was found unavoidable, in a case where what is substantially +a single theme has been treated in the various forms which it +assumed in the light of constantly growing knowledge. If the +critical reader finds this a defect, the author can plead in +extenuation only the difficulty of avoiding it under the +circumstances. Although mainly astronomical, a number of +discussions relating to general scientific subjects have been +included. + +Acknowledgment is due to the proprietors of the various +periodicals from the pages of which most of the essays have been +taken. Besides Harper's Magazine and the North American Review, +these include McClure's Magazine, from which were taken the +articles "The Unsolved Problems of Astronomy" and "How the Planets +are Weighed." "The Structure of the Universe" appeared in the +International Monthly, now the International Quarterly; "The +Outlook for the Flying-Machine" is mainly from The New York +Independent, but in part from McClure's Magazine; "The World's +Debt to Astronomy" is from The Chautauquan; and "An Astronomical +Friendship" from the Atlantic Monthly. + +SIMON NEWCOMB. WASHINGTON, JUNE, 1906. + + + + +I + +THE UNSOLVED PROBLEMS OF ASTRONOMY + + +The reader already knows what the solar system is: an immense +central body, the sun, with a number of planets revolving round it +at various distances. On one of these planets we dwell. Vast, +indeed, are the distances of the planets when measured by our +terrestrial standards. A cannon-ball fired from the earth to +celebrate the signing of the Declaration of Independence, and +continuing its course ever since with a velocity of eighteen +hundred feet per second, would not yet be half-way to the orbit of +Neptune, the outer planet. And yet the thousands of stars which +stud the heavens are at distances so much greater than that of +Neptune that our solar system is like a little colony, separated +from the rest of the universe by an ocean of void space almost +immeasurable in extent. The orbit of the earth round the sun is of +such size that a railway train running sixty miles an hour, with +never a stop, would take about three hundred and fifty years to +cross it. Represent this orbit by a lady's finger-ring. Then the +nearest fixed star will be about a mile and a half away; the next +more than two miles; a few more from three to twenty miles; the +great body at scores or hundreds of miles. Imagine the stars thus +scattered from the Atlantic to the Mississippi, and keep this +little finger-ring in mind as the orbit of the earth, and one may +have some idea of the extent of the universe. + +One of the most beautiful stars in the heavens, and one that can +be seen most of the year, is a Lyrae, or Alpha of the Lyre, known +also as Vega. In a spring evening it may be seen in the northeast, +in the later summer near the zenith, in the autumn in the +northwest. On the scale we have laid down with the earth's orbit +as a finger-ring, its distance would be some eight or ten miles. +The small stars around it in the same constellation are probably +ten, twenty, or fifty times as far. + +Now, the greatest fact which modern science has brought to light +is that our whole solar system, including the sun, with all its +planets, is on a journey towards the constellation Lyra. During +our whole lives, in all probability during the whole of human +history, we have been flying unceasingly towards this beautiful +constellation with a speed to which no motion on earth can +compare. The speed has recently been determined with a fair degree +of certainty, though not with entire exactness; it is about ten +miles a second, and therefore not far from three hundred millions +of miles a year. But whatever it may be, it is unceasing and +unchanging; for us mortals eternal. We are nearer the +constellation by five or six hundred miles every minute we live; +we are nearer to it now than we were ten years ago by thousands of +millions of miles, and every future generation of our race will be +nearer than its predecessor by thousands of millions of miles. + +When, where, and how, if ever, did this journey begin--when, +where, and how, if ever, will it end? This is the greatest of the +unsolved problems of astronomy. An astronomer who should watch the +heavens for ten thousand years might gather some faint suggestion +of an answer, or he might not. All we can do is to seek for some +hints by study and comparison with other stars. + +The stars are suns. To put it in another way, the sun is one of +the stars, and rather a small one at that. If the sun is moving in +the way I have described, may not the stars also be in motion, +each on a journey of its own through the wilderness of space? To +this question astronomy gives an affirmative answer. Most of the +stars nearest to us are found to be in motion, some faster than +the sun, some more slowly, and the same is doubtless true of all; +only the century of accurate observations at our disposal does not +show the motion of the distant ones. A given motion seems slower +the more distant the moving body; we have to watch a steamship on +the horizon some little time to see that she moves at all. Thus it +is that the unsolved problem of the motion of our sun is only one +branch of a yet more stupendous one: What mean the motions of the +stars--how did they begin, and how, if ever, will they end? So far +as we can yet see, each star is going straight ahead on its own +journey, without regard to its neighbors, if other stars can be so +called. Is each describing some vast orbit which, though looking +like a straight line during the short period of our observation, +will really be seen to curve after ten thousand or a hundred +thousand years, or will it go straight on forever? If the laws of +motion are true for all space and all time, as we are forced to +believe, then each moving star will go on in an unbending line +forever unless hindered by the attraction of other stars. If they +go on thus, they must, after countless years, scatter in all +directions, so that the inhabitants of each shall see only a +black, starless sky. + +Mathematical science can throw only a few glimmers of light on the +questions thus suggested. From what little we know of the masses, +distances, and numbers of the stars we see a possibility that the +more slow-moving ones may, in long ages, be stopped in their +onward courses or brought into orbits of some sort by the +attraction of their millions of fellows. But it is hard to admit +even this possibility in the case of the swift-moving ones. +Attraction, varying as the inverse square of the distance, +diminishes so rapidly as the distance increases that, at the +distances which separate the stars, it is small indeed. We could +not, with the most delicate balance that science has yet invented, +even show the attraction of the greatest known star. So far as we +know, the two swiftest-moving stars are, first, Arcturus, and, +second, one known in astronomy as 1830 Groombridge, the latter so +called because it was first observed by the astronomer +Groombridge, and is numbered 1830 in his catalogue of stars. If +our determinations of the distances of these bodies are to be +relied on, the velocity of their motion cannot be much less than +two hundred miles a second. They would make the circuit of the +earth every two or three minutes. A body massive enough to control +this motion would throw a large part of the universe into +disorder. Thus the problem where these stars came from and where +they are going is for us insoluble, and is all the more so from +the fact that the swiftly moving stars are moving in different +directions and seem to have no connection with each other or with +any known star. + +It must not be supposed that these enormous velocities seem so to +us. Not one of them, even the greatest, would be visible to the +naked eye until after years of watching. On our finger-ring scale, +1830 Groombridge would be some ten miles and Arcturus thirty or +forty miles away. Either of them would be moving only two or three +feet in a year. To the oldest Assyrian priests Lyra looked much as +it does to us to-day. Among the bright and well-known stars +Arcturus has the most rapid apparent motion, yet Job himself would +not to-day see that its position had changed, unless he had noted +it with more exactness than any astronomer of his time. + +Another unsolved problem among the greatest which present +themselves to the astronomer is that of the size of the universe +of stars. We know that several thousand of these bodies are +visible to the naked eye; moderate telescopes show us millions; +our giant telescopes of the present time, when used as cameras to +photograph the heavens, show a number past count, perhaps one +hundred millions. Are all these stars only those few which happen +to be near us in a universe extending out without end, or do they +form a collection of stars outside of which is empty infinite +space? In other words, has the universe a boundary? Taken in its +widest scope this question must always remain unanswered by us +mortals because, even if we should discover a boundary within +which all the stars and clusters we ever can know are contained, +and outside of which is empty space, still we could never prove +that this space is empty out to an infinite distance. Far outside +of what we call the universe might still exist other universes +which we can never see. + +It is a great encouragement to the astronomer that, although he +cannot yet set any exact boundary to this universe of ours, he is +gathering faint indications that it has a boundary, which his +successors not many generations hence may locate so that the +astronomer shall include creation itself within his mental grasp. +It can be shown mathematically that an infinitely extended system +of stars would fill the heavens with a blaze of light like that of +the noonday sun. As no such effect is produced, it may be +concluded that the universe has a boundary. But this does not +enable us to locate the boundary, nor to say how many stars may +lie outside the farthest stretches of telescopic vision. Yet by +patient research we are slowly throwing light on these points and +reaching inferences which, not many years ago, would have seemed +forever beyond our powers. + +Every one now knows that the Milky Way, that girdle of light which +spans the evening sky, is formed of clouds of stars too minute to +be seen by the unaided vision. It seems to form the base on which +the universe is built and to bind all the stars into a system. It +comprises by far the larger number of stars that the telescope has +shown to exist. Those we see with the naked eye are almost equally +scattered over the sky. But the number which the telescope shows +us become more and more condensed in the Milky Way as telescope +power is increased. The number of new stars brought out with our +greatest power is vastly greater in the Milky Way than in the rest +of the sky, so that the former contains a great majority of the +stars. What is yet more curious, spectroscopic research has shown +that a particular kind of stars, those formed of heated gas, are +yet more condensed in the central circle of this band; if they +were visible to the naked eye, we should see them encircling the +heavens as a narrow girdle forming perhaps the base of our whole +system of stars. This arrangement of the gaseous or vaporous stars +is one of the most singular facts that modern research has brought +to light. It seems to show that these particular stars form a +system of their own; but how such a thing can be we are still +unable to see. + +The question of the form and extent of the Milky Way thus becomes +the central one of stellar astronomy. Sir William Herschel began +by trying to sound its depths; at one time he thought he had +succeeded; but before he died he saw that they were unfathomable +with his most powerful telescopes. Even today he would be a bold +astronomer who would profess to say with certainty whether the +smallest stars we can photograph are at the boundary of the +system. Before we decide this point we must have some idea of the +form and distance of the cloudlike masses of stars which form our +great celestial girdle. A most curious fact is that our solar +system seems to be in the centre of this galactic universe, +because the Milky Way divides the heavens into two equal parts, +and seems equally broad at all points. Were we looking at such a +girdle as this from one side or the other, this appearance would +not be presented. But let us not be too bold. Perhaps we are the +victims of some fallacy, as Ptolemy was when he proved, by what +looked like sound reasoning, based on undeniable facts, that this +earth of ours stood at rest in the centre of the heavens! + +A related problem, and one which may be of supreme importance to +the future of our race, is, What is the source of the heat +radiated by the sun and stars? We know that life on the earth is +dependent on the heat which the sun sends it. If we were deprived +of this heat we should in a few days be enveloped in a frost which +would destroy nearly all vegetation, and in a few months neither +man nor animal would be alive, unless crouching over fires soon to +expire for want of fuel. We also know that, at a time which is +geologically recent, the whole of New England was covered with a +sheet of ice, hundreds or even thousands of feet thick, above +which no mountain but Washington raised its head. It is quite +possible that a small diminution in the supply of heat sent us by +the sun would gradually reproduce the great glacier, and once more +make the Eastern States like the pole. But the fact is that +observations of temperature in various countries for the last two +or three hundred years do not show any change in climate which can +be attributed to a variation in the amount of heat received from +the sun. + +The acceptance of this theory of the heat of those heavenly bodies +which shine by their own light--sun, stars, and nebulae--still +leaves open a problem that looks insoluble with our present +knowledge. What becomes of the great flood of heat and light which +the sun and stars radiate into empty space with a velocity of one +hundred and eighty thousand miles a second? Only a very small +fraction of it can be received by the planets or by other stars, +because these are mere points compared with their distance from +us. Taking the teaching of our science just as it stands, we +should say that all this heat continues to move on through +infinite space forever. In a few thousand years it reaches the +probable confines of our great universe. But we know of no reason +why it should stop here. During the hundreds of millions of years +since all our stars began to shine, has the first ray of light and +heat kept on through space at the rate of one hundred and eighty +thousand miles a second, and will it continue to go on for ages to +come? If so, think of its distance now, and think of its still +going on, to be forever wasted! Rather say that the problem, What +becomes of it? is as yet unsolved. + +Thus far I have described the greatest of problems; those which we +may suppose to concern the inhabitants of millions of worlds +revolving round the stars as much as they concern us. Let us now +come down from the starry heights to this little colony where we +live, the solar system. Here we have the great advantage of being +better able to see what is going on, owing to the comparative +nearness of the planets. When we learn that these bodies are like +our earth in form, size, and motions, the first question we ask +is, Could we fly from planet to planet and light on the surface of +each, what sort of scenery would meet our eyes? Mountain, forest, +and field, a dreary waste, or a seething caldron larger than our +earth? If solid land there is, would we find on it the homes of +intelligent beings, the lairs of wild beasts, or no living thing +at all? Could we breathe the air, would we choke for breath or be +poisoned by the fumes of some noxious gas? + +To most of these questions science cannot as yet give a positive +answer, except in the case of the moon. Our satellite is so near +us that we can see it has no atmosphere and no water, and +therefore cannot be the abode of life like ours. The contrast of +its eternal deadness with the active life around us is great +indeed. Here we have weather of so many kinds that we never tire +of talking about it. But on the moon there is no weather at all. +On our globe so many things are constantly happening that our +thousands of daily journals cannot begin to record them. But on +the dreary, rocky wastes of the moon nothing ever happens. So far +as we can determine, every stone that lies loose on its surface +has lain there through untold ages, unchanged and unmoved. + +We cannot speak so confidently of the planets. The most powerful +telescopes yet made, the most powerful we can ever hope to make, +would scarcely shows us mountains, or lakes, rivers, or fields at +a distance of fifty millions of miles. Much less would they show +us any works of man. Pointed at the two nearest planets, Venus and +Mars, they whet our curiosity more than they gratify it. +Especially is this the case with Venus. Ever since the telescope +was invented observers have tried to find the time of rotation of +this planet on its axis. Some have reached one conclusion, some +another, while the wisest have only doubted. The great Herschel +claimed that the planet was so enveloped in vapor or clouds that +no permanent features could be seen on its surface. The best +equipped recent observers think they see faint, shadowy patches, +which remain the same from day to day, and which show that the +planet always presents the same face to the sun, as the moon does +to the earth. Others do not accept this conclusion as proved, +believing that these patches may be nothing more than variations +of light, shade, and color caused by the reflection of the sun's +light at various angles from different parts of the planet. + +There is also some mystery about the atmosphere of this planet. +When Venus passes nearly between us and the sun, her dark +hemisphere is turned towards us, her bright one being always +towards the sun. But she is not exactly on a line with the sun +except on the very rare occasions of a transit across the sun's +disk. Hence, on ordinary occasions, when she seems very near on a +line with the sun, we see a very small part of the illuminated +hemisphere, which now presents the form of a very thin crescent +like the new moon. And this crescent is supposed to be a little +broader than it would be if only half the planet were illuminated, +and to encircle rather more than half the planet. Now, this is +just the effect that would be produced by an atmosphere refracting +the sun's light around the edge of the illuminated hemisphere. + +The difficulty of observations of this kind is such that the +conclusion may be open to doubt. What is seen during transits of +Venus over the sun's disk leads to more certain, but yet very +puzzling, conclusions. The writer will describe what he saw at the +Cape of Good Hope during the transit of December 5, 1882. As the +dark planet impinged on the bright sun, it of course cut out a +round notch from the edge of the sun. At first, when this notch +was small, nothing could be seen of the outline of that part of +the planet which was outside the sun. But when half the planet was +on the sun, the outline of the part still off the sun was marked +by a slender arc of light. A curious fact was that this arc did +not at first span the whole outline of the planet, but only showed +at one or two points. In a few moments another part of the outline +appeared, and then another, until, at last, the arc of light +extended around the complete outline. All this seems to show that +while the planet has an atmosphere, it is not transparent like +ours, but is so filled with mist and clouds that the sun is seen +through it only as if shining in a fog. + +Not many years ago the planet Mars, which is the next one outside +of us, was supposed to have a surface like that of our earth. Some +parts were of a dark greenish gray hue; these were supposed to be +seas and oceans. Other parts had a bright, warm tint; these were +supposed to be the continents. During the last twenty years much +has been learned as to how this planet looks, and the details of +its surface have been mapped by several observers, using the best +telescopes under the most favorable conditions of air and climate. +And yet it must be confessed that the result of this labor is not +altogether satisfactory. It seems certain that the so-called seas +are really land and not water. When it comes to comparing Mars +with the earth, we cannot be certain of more than a single point +of resemblance. This is that during the Martian winter a white +cap, as of snow, is formed over the pole, which partially melts +away during the summer. The conclusion that there are oceans whose +evaporation forms clouds which give rise to this snow seems +plausible. But the telescope shows no clouds, and nothing to make +it certain that there is an atmosphere to sustain them. There is +no certainty that the white deposit is what we call snow; perhaps +it is not formed of water at all. The most careful studies of the +surface of this planet, under the best conditions, are those made +at the Lowell Observatory at Flagstaff, Arizona. Especially +wonderful is the system of so-called canals, first seen by +Schiaparelli, but mapped in great detail at Flagstaff. But the +nature and meaning of these mysterious lines are still to be +discovered. The result is that the question of the real nature of +the surface of Mars and of what we should see around us could we +land upon it and travel over it are still among the unsolved +problems of astronomy. + +If this is the case with the nearest planets that we can study, +how is it with more distant ones? Jupiter is the only one of these +of the condition of whose surface we can claim to have definite +knowledge. But even this knowledge is meagre. The substance of +what we know is that its surface is surrounded by layers of what +look like dense clouds, through which nothing can certainly be +seen. + +I have already spoken of the heat of the sun and its probable +origin. But the question of its heat, though the most important, +is not the only one that the sun offers us. What is the sun? When +we say that it is a very hot globe, more than a million times as +large as the earth, and hotter than any furnace that man can make, +so that literally "the elements melt with fervent heat" even at +its surface, while inside they are all vaporized, we have told the +most that we know as to what the sun really is. Of course we know +a great deal about the spots, the rotation of the sun on its axis, +the materials of which it is composed, and how its surroundings +look during a total eclipse. But all this does not answer our +question. There are several mysteries which ingenious men have +tried to explain, but they cannot prove their explanations to be +correct. One is the cause and nature of the spots. Another is that +the shining surface of the sun, the "photosphere," as it is +technically called, seems so calm and quiet while forces are +acting within it of a magnitude quite beyond our conception. +Flames in which our earth and everything on it would be engulfed +like a boy's marble in a blacksmith's forge are continually +shooting up to a height of tens of thousands of miles. One would +suppose that internal forces capable of doing this would break the +surface up into billows of fire a thousand miles high; but we see +nothing of the kind. The surface of the sun seems almost as placid +as a lake. + +Yet another mystery is the corona of the sun. This is something we +should never have known to exist if the sun were not sometimes +totally eclipsed by the dark body of the moon. On these rare +occasions the sun is seen to be surrounded by a halo of soft, +white light, sending out rays in various directions to great +distances. This halo is called the corona, and has been most +industriously studied and photographed during nearly every total +eclipse for thirty years. Thus we have learned much about how it +looks and what its shape is. It has a fibrous, woolly structure, a +little like the loose end of a much-worn hempen rope. A certain +resemblance has been seen between the form of these seeming fibres +and that of the lines in which iron filings arrange themselves +when sprinkled on paper over a magnet. It has hence been inferred +that the sun has magnetic properties, a conclusion which, in a +general way, is supported by many other facts. Yet the corona +itself remains no less an unexplained phenomenon. + +[Illustration with caption: PHOTOGRAPH OF THE CORONA OF THE SUN, +TAKEN IN TRIPOLI DURING TOTAL ECLIPSE OF AUGUST 30, 1905] + +A phenomenon almost as mysterious as the solar corona is the +"zodiacal light," which any one can see rising from the western +horizon just after the end of twilight on a clear winter or spring +evening. The most plausible explanation is that it is due to a +cloud of small meteoric bodies revolving round the sun. We should +hardly doubt this explanation were it not that this light has a +yet more mysterious appendage, commonly called the Gegenschein, or +counter-glow. This is a patch of light in the sky in a direction +exactly opposite that of the sun. It is so faint that it can be +seen only by a practised eye under the most favorable conditions. +But it is always there. The latest suggestion is that it is a tail +of the earth, of the same kind as the tail of a comet! + +We know that the motions of the heavenly bodies are predicted with +extraordinary exactness by the theory of gravitation. When one +finds that the exact path of the moon's shadow on the earth during +a total eclipse of the sun can be mapped out many years in +advance, and that the planets follow the predictions of the +astronomer so closely that, if you could see the predicted planet +as a separate object, it would look, even in a good telescope, as +if it exactly fitted over the real planet, one thinks that here at +least is a branch of astronomy which is simply perfect. And yet +the worlds themselves show slight deviations in their movements +which the astronomer cannot always explain, and which may be due +to some hidden cause that, when brought to light, shall lead to +conclusions of the greatest importance to our race. + +One of these deviations is in the rotation of the earth. +Sometimes, for several years at a time, it seems to revolve a +little faster, and then again a little slower. The changes are +very slight; they can be detected only by the most laborious and +refined methods; yet they must have a cause, and we should like to +know what that cause is. + +The moon shows a similar irregularity of motion. For half a +century, perhaps through a whole century, she will go around the +earth a little ahead of her regular rate, and then for another +half-century or more she will fall behind. The changes are very +small; they would never have been seen with the unaided eye, yet +they exist. What is their cause? Mathematicians have vainly spent +years of study in trying to answer this question. + +The orbit of Mercury is found by observations to have a slight +motion which mathematicians have vainly tried to explain. For some +time it was supposed to be caused by the attraction of an unknown +planet between Mercury and the sun, and some were so sure of the +existence of this planet that they gave it a name, calling it +Vulcan. But of late years it has become reasonably certain that no +planet large enough to produce the effect observed can be there. +So thoroughly has every possible explanation been sifted out and +found wanting, that some astronomers are now inquiring whether the +law of gravitation itself may not be a little different from what +has always been supposed. A very slight deviation, indeed, would +account for the facts, but cautious astronomers want other proofs +before regarding the deviation of gravitation as an established +fact. + +Intelligent men have sometimes inquired how, after devoting so +much work to the study of the heavens, anything can remain for +astronomers to find out. It is a curious fact that, although they +were never learning so fast as at the present day, yet there seems +to be more to learn now than there ever was before. Great and +numerous as are the unsolved problems of our science, knowledge is +now advancing into regions which, a few years ago, seemed +inaccessible. Where it will stop none can say. + + + + + +II + +THE NEW PROBLEMS OF THE UNIVERSE + + +The achievements of the nineteenth century are still a theme of +congratulation on the part of all who compare the present state of +the world with that of one hundred years ago. And yet, if we +should fancy the most sagacious prophet, endowed with a brilliant +imagination, to have set forth in the year 1806 the problems that +the century might solve and the things which it might do, we +should be surprised to see how few of his predictions had come to +pass. He might have fancied aerial navigation and a number of +other triumphs of the same class, but he would hardly have had +either steam navigation or the telegraph in his picture. In 1856 +an article appeared in Harper's Magazine depicting some +anticipated features of life in A.D. 3000. We have since made +great advances, but they bear little resemblance to what the +writer imagined. He did not dream of the telephone, but did +describe much that has not yet come to pass and probably never +will. + +The fact is that, much as the nineteenth century has done, its +last work was to amuse itself by setting forth more problems for +this century to solve than it has ever itself succeeded in +mastering. We should not be far wrong in saying that to-day there +are more riddles in the universe than there were before men knew +that it contained anything more than the objects they could see. + +So far as mere material progress is concerned, it may be doubtful +whether anything so epoch-making as the steam-engine or the +telegraph is held in store for us by the future. But in the field +of purely scientific discovery we are finding a crowd of things of +which our philosophy did not dream even ten years ago. + +The greatest riddles which the nineteenth century has bequeathed +to us relate to subjects so widely separated as the structure of +the universe and the structure of atoms of matter. We see more and +more of these structures, and we see more and more of unity +everywhere, and yet new facts difficult of explanation are being +added more rapidly than old facts are being explained. + +We all know that the nineteenth century was marked by a separation +of the sciences into a vast number of specialties, to the +subdivisions of which one could see no end. But the great work of +the twentieth century will be to combine many of these +specialties. The physical philosopher of the present time is +directing his thought to the demonstration of the unity of +creation. Astronomical and physical researches are now being +united in a way which is bringing the infinitely great and the +infinitely small into one field of knowledge. Ten years ago the +atoms of matter, of which it takes millions of millions to make a +drop of water, were the minutest objects with which science could +imagine itself to be concerned, Now a body of experimentalists, +prominent among whom stand Professors J. J. Thompson, Becquerel, +and Roentgen, have demonstrated the existence of objects so minute +that they find their way among and between the atoms of matter as +rain-drops do among the buildings of a city. More wonderful yet, +it seems likely, although it has not been demonstrated, that these +little things, called "corpuscles," play an important part in what +is going on among the stars. Whether this be true or not, it is +certain that there do exist in the universe emanations of some +sort, producing visible effects, the investigation of which the +nineteenth century has had to bequeath to the twentieth. + +For the purpose of the navigator, the direction of the magnetic +needle is invariable in any one place, for months and even years; +but when exact scientific observations on it are made, it is found +subject to numerous slight changes. The most regular of these +consists in a daily change of its direction. It moves one way from +morning until noon, and then, late in the afternoon and during the +night, turns back again to its original pointing. The laws of this +change have been carefully studied from observations, which show +that it is least at the equator and larger as we go north into +middle latitudes; but no explanation of it resting on an +indisputable basis has ever been offered. + +Besides these regular changes, there are others of a very +irregular character. Every now and then the changes in the +direction of the magnet are wider and more rapid than those which +occur regularly every day. The needle may move back and forth in a +way so fitful as to show the action of some unusual exciting +cause. Such movements of the needle are commonly seen when there +is a brilliant aurora. This connection shows that a magnetic storm +and an aurora must be due to the same or some connected causes. + +Those of us who are acquainted with astronomical matters know that +the number of spots on the sun goes through a regular cycle of +change, having a period of eleven years and one or two months. +Now, the curious fact is, when the number and violence of magnetic +storms are recorded and compared, it is found that they correspond +to the spots on the sun, and go through the same period of eleven +years. The conclusion seems almost inevitable: magnetic storms are +due to some emanation sent out by the sun, which arises from the +same cause that produces the spots. This emanation does not go on +incessantly, but only in an occasional way, as storms follow each +other on the earth. What is it? Every attempt to detect it has +been in vain. Professor Hale, at the Yerkes Observatory, has had +in operation from time to time, for several years, his ingenious +spectroheliograph, which photographs the sun by a single ray of +the spectrum. This instrument shows that violent actions are going +on in the sun, which ordinary observation would never lead us to +suspect. But it has failed to show with certainty any peculiar +emanation at the time of a magnetic storm or anything connected +with such a storm. + +A mystery which seems yet more impenetrable is associated with the +so-called new stars which blaze forth from time to time. These +offer to our sight the most astounding phenomena ever presented to +the physical philosopher. One hundred years ago such objects +offered no mystery. There was no reason to suppose that the +Creator of the universe had ceased His functions; and, continuing +them, it was perfectly natural that He should be making continual +additions to the universe of stars. But the idea that these +objects are really new creations, made out of nothing, is contrary +to all our modern ideas and not in accord with the observed facts. +Granting the possibility of a really new star--if such an object +were created, it would be destined to take its place among the +other stars as a permanent member of the universe. Instead of +this, such objects invariably fade away after a few months, and +are changed into something very like an ordinary nebula. A +question of transcendent interest is that of the cause of these +outbursts. It cannot be said that science has, up to the present +time, been able to offer any suggestion not open to question. The +most definite one is the collision theory, according to which the +outburst is due to the clashing together of two stars, one or both +of which might previously have been dark, like a planet. The stars +which may be actually photographed probably exceed one hundred +millions in number, and those which give too little light to +affect the photographic plate may be vastly more numerous than +those which do. Dark stars revolve around bright ones in an +infinite variety of ways, and complex systems of bodies, the +members of which powerfully attract each other, are the rule +throughout the universe. Moreover, we can set no limit to the +possible number of dark or invisible stars that may be flying +through the celestial spaces. While, therefore, we cannot regard +the theory of collision as established, it seems to be the only +one yet put forth which can lay any claim to a scientific basis. +What gives most color to it is the extreme suddenness with which +the new stars, so far as has yet been observed, invariably blaze +forth. In almost every case it has been only two or three days +from the time that the existence of such an object became known +until it had attained nearly its full brightness. In fact, it +would seem that in the case of the star in Perseus, as in most +other cases, the greater part of the outburst took place within +the space of twenty-four hours. This suddenness and rapidity is +exactly what would be the result of a collision. + +The most inexplicable feature of all is the rapid formation of a +nebula around this star. In the first photographs of the latter, +the appearance presented is simply that of an ordinary star. But, +in the course of three or four months, the delicate photographs +taken at the Lick Observatory showed that a nebulous light +surrounded the star, and was continually growing larger and +larger. At first sight, there would seem to be nothing +extraordinary in this fact. Great masses of intensely hot vapor, +shining by their own light, would naturally be thrown out from the +star. Or, if the star had originally been surrounded by a very +rare nebulous fog or vapor, the latter would be seen by the +brilliant light emitted by the star. On this was based an +explanation offered by Kapteyn, which at first seemed very +plausible. It was that the sudden wave of light thrown out by the +star when it burst forth caused the illumination of the +surrounding vapor, which, though really at rest, would seem to +expand with the velocity of light, as the illumination reached +more and more distant regions of the nebula. This result may be +made the subject of exact calculation. The velocity of light is +such as would make a circuit of the earth more than seven times in +a second. It would, therefore, go out from the star at the rate of +a million of miles in between five and six seconds. In the lapse +of one of our days, the light would have filled a sphere around +the star having a diameter more than one hundred and fifty times +the distance of the sun from the earth, and more than five times +the dimensions of the whole solar system. Continuing its course +and enlarging its sphere day after day, the sight presented to us +would have been that of a gradually expanding nebulous mass--a +globe of faint light continually increasing in size with the +velocity of light. + +The first sentiment the reader will feel on this subject is +doubtless one of surprise that the distance of the star should be +so great as this explanation would imply. Six months after the +explosion, the globe of light, as actually photographed, was of a +size which would have been visible to the naked eye only as a very +minute object in the sky. Is it possible that this minute object +could have been thousands of times the dimensions of our solar +system? + +To see how the question stands from this point of view, we must +have some idea of the possible distance of the new star. To gain +this idea, we must find some way of estimating distances in the +universe. For a reason which will soon be apparent, we begin with +the greatest structure which nature offers to the view of man. We +all know that the Milky Way is formed of countless stars, too +minute to be individually visible to the naked eye. The more +powerful the telescope through which we sweep the heavens, the +greater the number of the stars that can be seen in it. With the +powerful instruments which are now in use for photographing the +sky, the number of stars brought to light must rise into the +hundreds of millions, and the greater part of these belong to the +Milky Way. The smaller the stars we count, the greater their +comparative number in the region of the Milky Way. Of the stars +visible through the telescope, more than one-half are found in the +Milky Way, which may be regarded as a girdle spanning the entire +visible universe. + +Of the diameter of this girdle we can say, almost with certainty, +that it must be more than a thousand times as great as the +distance of the nearest fixed star from us, and is probably two or +three times greater. According to the best judgment we can form, +our solar system is situate near the central region of the girdle, +so that the latter must be distant from us by half its diameter. +It follows that if we can imagine a gigantic pair of compasses, of +which the points extend from us to Alpha Centauri, the nearest +star, we should have to measure out at least five hundred spaces +with the compass, and perhaps even one thousand or more, to reach +the region of the Milky Way. + +With this we have to connect another curious fact. Of eighteen new +stars which have been observed to blaze forth during the last four +hundred years, all are in the region of the Milky Way. This seems +to show that, as a rule, they belong to the Milky Way. Accepting +this very plausible conclusion, the new star in Perseus must have +been more than five hundred times as far as the nearest fixed +star. We know that it takes light four years to reach us from +Alpha Centauri. It follows that the new star was at a distance +through which light would require more than two thousand years to +travel, and quite likely a time two or three times this. It +requires only the most elementary ideas of geometry to see that if +we suppose a ray of light to shoot from a star at such a distance +in a direction perpendicular to the line of sight from us to the +star, we can compute how fast the ray would seem to us to travel. +Granting the distance to be only two thousand light years, the +apparent size of the sphere around the star which the light would +fill at the end of one year after the explosion would be that of a +coin seen at a distance of two thousand times its radius, or one +thousand times its diameter--say, a five-cent piece at the +distance of sixty feet. But, as a matter of fact, the nebulous +illumination expanded with a velocity from ten to twenty times as +great as this. + +The idea that the nebulosity around the new star was formed by the +illumination caused by the light of the explosion spreading out on +all sides therefore fails to satisfy us, not because the expansion +of the nebula seemed to be so slow, but because it was many times +as swift as the speed of light. Another reason for believing that +it was not a mere wave of light is offered by the fact that it did +not take place regularly in every direction from the star, but +seemed to shoot off at various angles. + +Up to the present time, the speed of light has been to science, as +well as to the intelligence of our race, almost a symbol of the +greatest of possible speeds. The more carefully we reflect on the +case, the more clearly we shall see the difficulty in supposing +any agency to travel at the rate of the seeming emanations from +the new star in Perseus. + +As the emanation is seen spreading day after day, the reader may +inquire whether this is not an appearance due to some other cause +than the mere motion of light. May not an explosion taking place +in the centre of a star produce an effect which shall travel yet +faster than light? We can only reply that no such agency is known +to science. + +But is there really anything intrinsically improbable in an agency +travelling with a speed many times that of light? In considering +that there is, we may fall into an error very much like that into +which our predecessors fell in thinking it entirely out of the +range of reasonable probability that the stars should be placed at +such distances as we now know them to be. + +Accepting it as a fact that agencies do exist which travel from +sun to planet and from star to star with a speed which beggars all +our previous ideas, the first question that arises is that of +their nature and mode of action. This question is, up to the +present time, one which we do not see any way of completely +answering. The first difficulty is that we have no evidence of +these agents except that afforded by their action. We see that the +sun goes through a regular course of pulsations, each requiring +eleven years for completion; and we see that, simultaneously with +these, the earth's magnetism goes through a similar course of +pulsations. The connection of the two, therefore, seems absolutely +proven. But when we ask by what agency it is possible for the sun +to affect the magnetism of the earth, and when we trace the +passage of some agent between the two bodies, we find nothing to +explain the action. To all appearance, the space between the earth +and the sun is a perfect void. That electricity cannot of itself +pass through a vacuum seems to be a well-established law of +physics. It is true that electromagnetic waves, which are supposed +to be of the same nature with those of light, and which are used +in wireless telegraphy, do pass through a vacuum and may pass from +the sun to the earth. But there is no way of explaining how such +waves would either produce or affect the magnetism of the earth. + +The mysterious emanations from various substances, under certain +conditions, may have an intimate relation with yet another of the +mysteries of the universe. It is a fundamental law of the universe +that when a body emits light or heat, or anything capable of being +transformed into light or heat, it can do so only by the +expenditure of force, limited in supply. The sun and stars are +continually sending out a flood of heat. They are exhausting the +internal supply of something which must be limited in extent. +Whence comes the supply? How is the heat of the sun kept up? If it +were a hot body cooling off, a very few years would suffice for it +to cool off so far that its surface would become solid and very +soon cold. In recent years, the theory universally accepted has +been that the supply of heat is kept up by the continual +contraction of the sun, by mutual gravitation of its parts as it +cools off. This theory has the advantage of enabling us to +calculate, with some approximation to exactness, at what rate the +sun must be contracting in order to keep up the supply of heat +which it radiates. On this theory, it must, ten millions of years +ago, have had twice its present diameter, while less than twenty +millions of years ago it could not have existed except as an +immense nebula filling the whole solar system. We must bear in +mind that this theory is the only one which accounts for the +supply of heat, even through human history. If it be true, then +the sun, earth, and solar system must be less than twenty million +years old. + +Here the geologists step in and tell us that this conclusion is +wholly inadmissible. The study of the strata of the earth and of +many other geological phenomena, they assure us, makes it certain +that the earth must have existed much in its present condition for +hundreds of millions of years. During all that time there can have +been no great diminution in the supply of heat radiated by the +sun. + +The astronomer, in considering this argument, has to admit that he +finds a similar difficulty in connection with the stars and +nebulas. It is an impossibility to regard these objects as new; +they must be as old as the universe itself. They radiate heat and +light year after year. In all probability, they must have been +doing so for millions of years. Whence comes the supply? The +geologist may well claim that until the astronomer explains this +mystery in his own domain, he cannot declare the conclusions of +geology as to the age of the earth to be wholly inadmissible. + +Now, the scientific experiments of the last two years have brought +this mystery of the celestial spaces right down into our earthly +laboratories. M. and Madame Curie have discovered the singular +metal radium, which seems to send out light, heat, and other rays +incessantly, without, so far as has yet been determined, drawing +the required energy from any outward source. As we have already +pointed out, such an emanation must come from some storehouse of +energy. Is the storehouse, then, in the medium itself, or does the +latter draw it from surrounding objects? If it does, it must +abstract heat from these objects. This question has been settled +by Professor Dewar, at the Royal Institution, London, by placing +the radium in a medium next to the coldest that art has yet +produced--liquid air. The latter is surrounded by the only yet +colder medium, liquid hydrogen, so that no heat can reach it. +Under these circumstances, the radium still gives out heat, +boiling away the liquid air until the latter has entirely +disappeared. Instead of the radiation diminishing with time, it +rather seems to increase. + +Called on to explain all this, science can only say that a +molecular change must be going on in the radium, to correspond to +the heat it gives out. What that change may be is still a complete +mystery. It is a mystery which we find alike in those minute +specimens of the rarest of substances under our microscopes, in +the sun, and in the vast nebulous masses in the midst of which our +whole solar system would be but a speck. The unravelling of this +mystery must be the great work of science of the twentieth +century. What results shall follow for mankind one cannot say, any +more than he could have said two hundred years ago what modern +science would bring forth. Perhaps, before future developments, +all the boasted achievements of the nineteenth century may take +the modest place which we now assign to the science of the +eighteenth century--that of the infant which is to grow into a +man. + + + + + +III + +THE STRUCTURE OF THE UNIVERSE + + +The questions of the extent of the universe in space and of its +duration in time, especially of its possible infinity in either +space or time, are of the highest interest both in philosophy and +science. The traditional philosophy had no means of attacking +these questions except considerations suggested by pure reason, +analogy, and that general fitness of things which was supposed to +mark the order of nature. With modern science the questions belong +to the realm of fact, and can be decided only by the results of +observation and a study of the laws to which these results may +lead. + +From the philosophic stand-point, a discussion of this subject +which is of such weight that in the history of thought it must be +assigned a place above all others, is that of Kant in his +"Kritik." Here we find two opposing propositions--the thesis that +the universe occupies only a finite space and is of finite +duration; the antithesis that it is infinite both as regards +extent in space and duration in time. Both of these opposing +propositions are shown to admit of demonstration with equal force, +not directly, but by the methods of reductio ad absurdum. The +difficulty, discussed by Kant, was more tersely expressed by +Hamilton in pointing out that we could neither conceive of +infinite space nor of space as bounded. The methods and +conclusions of modern astronomy are, however, in no way at +variance with Kant's reasoning, so far as it extends. The fact is +that the problem with which the philosopher of Konigsberg vainly +grappled is one which our science cannot solve any more than could +his logic. We may hope to gain complete information as to +everything which lies within the range of the telescope, and to +trace to its beginning every process which we can now see going on +in space. But before questions of the absolute beginning of +things, or of the boundary beyond which nothing exists, our means +of inquiry are quite powerless. + +Another example of the ancient method is found in the great work +of Copernicus. It is remarkable how completely the first expounder +of the system of the world was dominated by the philosophy of his +time, which he had inherited from his predecessors. This is seen +not only in the general course of thought through the opening +chapters of his work, but among his introductory propositions. The +first of these is that the universe--mundus--as well as the earth, +is spherical in form. His arguments for the sphericity of the +earth, as derived from observation, are little more than a +repetition of those of Ptolemy, and therefore not of special +interest. His proposition that the universe is spherical is, +however, not based on observation, but on considerations of the +perfection of the spherical form, the general tendency of bodies-- +a drop of water, for example--to assume this form, and the +sphericity of the sun and moon. The idea retained its place in his +mind, although the fundamental conception of his system did away +with the idea of the universe having any well-defined form. + +The question as attacked by modern astronomy is this: we see +scattered through space in every direction many millions of stars +of various orders of brightness and at distances so great as to +defy exact measurement, except in the case of a few of the +nearest. Has this collection of stars any well-defined boundary, +or is what we see merely that part of an infinite mass which +chances to lie within the range of our telescopes? If we were +transported to the most distant star of which we have knowledge, +should we there find ourselves still surrounded by stars on all +sides, or would the space beyond be void? Granting that, in any or +every direction, there is a limit to the universe, and that the +space beyond is therefore void, what is the form of the whole +system and the distance of its boundaries? Preliminary in some +sort to these questions are the more approachable ones: Of what +sort of matter is the universe formed? and into what sort of +bodies is this matter collected? + +To the ancients the celestial sphere was a reality, instead of a +mere effect of perspective, as we regard it. The stars were set on +its surface, or at least at no great distance within its +crystalline mass. Outside of it imagination placed the empyrean. +When and how these conceptions vanished from the mind of man, it +would be as hard to say as when and how Santa Claus gets +transformed in the mind of the child. They are not treated as +realities by any astronomical writer from Ptolemy down; yet, the +impressions and forms of thought to which they gave rise are well +marked in Copernicus and faintly evident in Kepler. The latter was +perhaps the first to suggest that the sun might be one of the +stars; yet, from defective knowledge of the relative brightness of +the latter, he was led to the conclusion that their distances from +each other were less than the distance which separated them from +the sun. The latter he supposed to stand in the centre of a vast +vacant region within the system of stars. + +For us the great collection of millions of stars which are made +known to us by the telescope, together with all the invisible +bodies which may be contained within the limits of the system, +form the universe. Here the term "universe" is perhaps +objectionable because there may be other systems than the one with +which we are acquainted. The term stellar system is, therefore, a +better one by which to designate the collection of stars in +question. + +It is remarkable that the first known propounder of that theory of +the form and arrangement of the system which has been most +generally accepted seems to have been a writer otherwise unknown +in science--Thomas Wright, of Durham, England. He is said to have +published a book on the theory of the universe, about 1750. It +does not appear that this work was of a very scientific character, +and it was, perhaps, too much in the nature of a speculation to +excite notice in scientific circles. One of the curious features +of the history is that it was Kant who first cited Wright's +theory, pointed out its accordance with the appearance of the +Milky Way, and showed its general reasonableness. But, at the time +in question, the work of the philosopher of Konigsberg seems to +have excited no more notice among his scientific contemporaries +than that of Wright. + +Kant's fame as a speculative philosopher has so eclipsed his +scientific work that the latter has but recently been appraised at +its true value. He was the originator of views which, though +defective in detail, embodied a remarkable number of the results +of recent research on the structure and form of the universe, and +the changes taking place in it. The most curious illustration of +the way in which he arrived at a correct conclusion by defective +reasoning is found in his anticipation of the modern theory of a +constant retardation of the velocity with which the earth revolves +on its axis. He conceived that this effect must result from the +force exerted by the tidal wave, as moving towards the west it +strikes the eastern coasts of Asia and America. An opposite +conclusion was reached by Laplace, who showed that the effect of +this force was neutralized by forces producing the wave and acting +in the opposite direction. And yet, nearly a century later, it was +shown that while Laplace was quite correct as regards the general +principles involved, the friction of the moving water must prevent +the complete neutralization of the two opposing forces, and leave +a small residual force acting towards the west and retarding the +rotation. Kant's conclusion was established, but by an action +different from that which he supposed. + +The theory of Wright and Kant, which was still further developed +by Herschel, was that our stellar system has somewhat the form of +a flattened cylinder, or perhaps that which the earth would assume +if, in consequence of more rapid rotation, the bulging out at its +equator and the flattening at its poles were carried to an extreme +limit. This form has been correctly though satirically compared to +that of a grindstone. It rests to a certain extent, but not +entirely, on the idea that the stars are scattered through space +with equal thickness in every direction, and that the appearance +of the Milky Way is due to the fact that we, situated in the +centre of this flattened system, see more stars in the direction +of the circumference of the system than in that of its poles. The +argument on which the view in question rests may be made clear in +the following way. + +Let us chose for our observations that hour of the night at which +the Milky Way skirts our horizon. This is nearly the case in the +evenings of May and June, though the coincidence with the horizon +can never be exact except to observers stationed near the tropics. +Using the figure of the grindstone, we at its centre will then +have its circumference around our horizon, while the axis will be +nearly vertical. The points in which the latter intersects the +celestial sphere are called the galactic poles. There will be two +of these poles, the one at the hour in question near the zenith, +the other in our nadir, and therefore invisible to us, though seen +by our antipodes. Our horizon corresponds, as it were, to the +central circle of the Milky Way, which now surrounds us on all +sides in a horizontal direction, while the galactic poles are 90 +degrees distant from every part of it, as every point of the +horizon is 90 degrees from the zenith. + +Let us next count the number of stars visible in a powerful +telescope in the region of the heavens around the galactic pole, +now our zenith, and find the average number per square degree. +This will be the richness of the region in stars. Then we take +regions nearer the horizontal Milky Way--say that contained +between 10 degrees and 20 degrees from the zenith--and, by a +similar count, find its richness in stars. We do the same for +other regions, nearer and nearer to the horizon, till we reach the +galaxy itself. The result of all the counts will be that the +richness of the sky in stars is least around the galactic pole, +and increases in every direction towards the Milky Way. + +Without such counts of the stars we might imagine our stellar +system to be a globular collection of stars around which the +object in question passed as a girdle; and we might take a globe +with a chain passing around it as representative of the possible +figure of the stellar system. But the actual increase in star- +thickness which we have pointed out shows us that this view is +incorrect. The nature and validity of the conclusions to be drawn +can be best appreciated by a statement of some features of this +tendency of the stars to crowd towards the galactic circle. + +Most remarkable is the fact that the tendency is seen even among +the brighter stars. Without either telescope or technical +knowledge, the careful observer of the stars will notice that the +most brilliant constellations show this tendency. The glorious +Orion, Canis Major containing the brightest star in the heavens, +Cassiopeia, Perseus, Cygnus, and Lyra with its bright-blue Vega, +not to mention such constellations as the Southern Cross, all lie +in or near the Milky Way. Schiaparelli has extended the +investigation to all the stars visible to the naked eye. He laid +down on planispheres the number of such stars in each region of +the heavens of 5 degrees square. Each region was then shaded with +a tint that was darker as the region was richer in stars. The very +existence of the Milky Way was ignored in this work, though his +most darkly shaded regions lie along the course of this belt. By +drawing a band around the sky so as to follow or cover his darkest +regions, we shall rediscover the course of the Milky Way without +any reference to the actual object. It is hardly necessary to add +that this result would be reached with yet greater precision if we +included the telescopic stars to any degree of magnitude--plotting +them on a chart and shading the chart in the same way. What we +learn from this is that the stellar system is not an irregular +chaos; and that notwithstanding all its minor irregularities, it +may be considered as built up with special reference to the Milky +Way as a foundation. + +Another feature of the tendency in question is that it is more and +more marked as we include fainter stars in our count. The galactic +region is perhaps twice as rich in stars visible to the naked eye +as the rest of the heavens. In telescopic stars to the ninth +magnitude it is three or four times as rich. In the stars found on +the photographs of the sky made at the Harvard and other +observatories, and in the stargauges of the Herschels, it is from +five to ten times as rich. + +Another feature showing the unity of the system is the symmetry of +the heavens on the two sides of the galactic belt Let us return to +our supposition of such a position of the celestial sphere, with +respect to the horizon, that the latter coincides with the central +line of this belt, one galactic pole being near our zenith. The +celestial hemisphere which, being above our horizon, is visible to +us, is the one to which we have hitherto directed our attention in +describing the distribution of the stars. But below our horizon is +another hemisphere, that of our antipodes, which is the +counterpart of ours. The stars which it contains are in a +different part of the universe from those which we see, and, +without unity of plan, would not be subject to the same law. But +the most accurate counts of stars that have been made fail to show +any difference in their general arrangement in the two +hemispheres. They are just as thick around the south galactic +poles as around the north one. They show the same tendency to +crowd towards the Milky Way in the hemisphere invisible to us as +in the hemisphere which we see. Slight differences and +irregularities, are, indeed, found in the enumeration, but they +are no greater than must necessarily arise from the difficulty of +stopping our count at a perfectly fixed magnitude. The aim of +star-counts is not to estimate the total number of stars, for this +is beyond our power, but the number visible with a given +telescope. In such work different observers have explored +different parts of the sky, and in a count of the same region by +two observers we shall find that, although they attempt to stop at +the same magnitude, each will include a great number of stars +which the other omits. There is, therefore, room for considerable +difference in the numbers of stars recorded, without there being +any actual inequality between the two hemispheres. + +A corresponding similarity is found in the physical constitution +of the stars as brought out by the spectroscope. The Milky Way is +extremely rich in bluish stars, which make up a considerable +majority of the cloudlike masses there seen. But when we recede +from the galaxy on one side, we find the blue stars becoming +thinner, while those having a yellow tinge become relatively more +numerous. This difference of color also is the same on the two +sides of the galactic plane. Nor can any systematic difference be +detected between the proper motions of the stars in these two +hemispheres. If the largest known proper motion is found in the +one, the second largest is in the other. Counting all the known +stars that have proper motions exceeding a given limit, we find +about as many in one hemisphere as in the other. In this respect, +also, the universe appears to be alike through its whole extent. +It is the uniformity thus prevailing through the visible universe, +as far as we can see, in two opposite directions, which inspires +us with confidence in the possibility of ultimately reaching some +well-founded conclusion as to the extent and structure of the +system. + +All these facts concur in supporting the view of Wright, Kant, and +Herschel as to the form of the universe. The farther out the stars +extend in any direction, the more stars we may see in that +direction. In the direction of the axis of the cylinder, the +distances of the boundary are least, so that we see fewer stars. +The farther we direct our attention towards the equatorial regions +of the system, the greater the distance from us to the boundary, +and hence the more stars we see. The fact that the increase in the +number of stars seen towards the equatorial region of the system +is greater, the smaller the stars, is the natural consequence of +the fact that distant stars come within our view in greater +numbers towards the equatorial than towards the polar regions. + +Objections have been raised to the Herschelian view on the ground +that it assumes an approximately uniform distribution of the stars +in space. It has been claimed that the fact of our seeing more +stars in one direction than in another may not arise merely from +our looking through a deeper stratum, as Herschel supposed, but +may as well be due to the stars being more thinly scattered in the +direction of the axis of the system than in that of its equatorial +region. The great inequalities in the richness of neighboring +regions in the Milky Way show that the hypothesis of uniform +distribution does not apply to the equatorial region. The claim +has therefore been made that there is no proof of the system +extending out any farther in the equatorial than in the polar +direction. + +The consideration of this objection requires a closer inquiry as +to what we are to understand by the form of our system. We have +already pointed out the impossibility of assigning any boundary +beyond which we can say that nothing exists. And even as regards a +boundary of our stellar system, it is impossible for us to assign +any exact limit beyond which no star is visible to us. The analogy +of collections of stars seen in various parts of the heavens leads +us to suppose that there may be no well-defined form to our +system, but that, as we go out farther and farther, we shall see +occasional scattered stars to, possibly, an indefinite distance. +The truth probably is that, as in ascending a mountain, we find +the trees, which may be very dense at its base, thin out gradually +as we approach the summit, where there may be few or none, so we +might find the stars to thin out could we fly to the distant +regions of space. The practical question is whether, in such a +flight, we should find this sooner by going in the direction of +the axis of our system than by directing our course towards the +Milky Way. If a point is at length reached beyond which there are +but few scattered stars, such a point would, for us, mark the +boundary of our system. From this point of view the answer does +not seem to admit of doubt. If, going in every direction, we mark +the point, if any, at which the great mass of the stars are seen +behind us, the totality of all these points will lie on a surface +of the general form that Herschel supposed. + +There is still another direct indication of the finitude of our +stellar system upon which we have not touched. If this system +extended out without limit in any direction whatever, it is shown +by a geometric process which it is not necessary to explain in the +present connection, but which is of the character of mathematical +demonstration, that the heavens would, in every direction where +this was true, blaze with the light of the noonday sun. This would +be very different from the blue-black sky which we actually see on +a clear night, and which, with a reservation that we shall +consider hereafter, shows that, how far so-ever our stellar +system may extend, it is not infinite. Beyond this negative +conclusion the fact does not teach us much. Vast, indeed, is the +distance to which the system might extend without the sky +appearing much brighter than it is, and we must have recourse to +other considerations in seeking for indications of a boundary, or +even of a well-marked thinning out, of stars. + +If, as was formerly supposed, the stars did not greatly differ in +the amount of light emitted by each, and if their diversity of +apparent magnitude were due principally to the greater distance of +the fainter stars, then the brightness of a star would enable us +to form a more or less approximate idea of its distance. But the +accumulated researches of the past seventy years show that the +stars differ so enormously in their actual luminosity that the +apparent brightness of a star affords us only a very imperfect +indication of its distance. While, in the general average, the +brighter stars must be nearer to us than the fainter ones, it by +no means follows that a very bright star, even of the first +magnitude, is among the nearer to our system. Two stars are worthy +of especial mention in this connection, Canopus and Rigel. The +first is, with the single exception of Sirius, the brightest star +in the heavens. The other is a star of the first magnitude in the +southwest corner of Orion. The most long-continued and complete +measures of parallax yet made are those carried on by Gill, at the +Cape of Good Hope, on these two and some other bright stars. The +results, published in 1901, show that neither of these bodies has +any parallax that can be measured by the most refined instrumental +means known to astronomy. In other words, the distance of these +stars is immeasurably great. The actual amount of light emitted by +each is certainly thousands and probably tens of thousands of +times that of the sun. + +Notwithstanding the difficulties that surround the subject, we can +at least say something of the distance of a considerable number of +the stars. Two methods are available for our estimate--measures of +parallax and determination of proper motions. + +The problem of stellar parallax, simple though it is in its +conception, is the most delicate and difficult of all which the +practical astronomer has to encounter. An idea of it may be gained +by supposing a minute object on a mountain-top, we know not how +many miles away, to be visible through a telescope. The observer +is allowed to change the position of his instrument by two inches, +but no more. He is required to determine the change in the +direction of the object produced by this minute displacement with +accuracy enough to determine the distance of the mountain. This is +quite analogous to the determination of the change in the +direction in which we see a star as the earth, moving through its +vast circuit, passes from one extremity of its orbit to the other. +Representing this motion on such a scale that the distance of our +planet from the sun shall be one inch, we find that the nearest +star, on the same scale, will be more than four miles away, and +scarcely one out of a million will be at a less distance than ten +miles. It is only by the most wonderful perfection both in the +heliometer, the instrument principally used for these measures, +and in methods of observation, that any displacement at all can be +seen even among the nearest stars. The parallaxes of perhaps a +hundred stars have been determined, with greater or less +precision, and a few hundred more may be near enough for +measurement. All the others are immeasurably distant; and it is +only by statistical methods based on their proper motions and +their probable near approach to equality in distribution that any +idea can be gained of their distances. + +To form a conception of the stellar system, we must have a unit of +measure not only exceeding any terrestrial standard, but even any +distance in the solar system. For purely astronomical purposes the +most convenient unit is the distance corresponding to a parallax +of 1", which is a little more than 200,000 times the sun's +distance. But for the purposes of all but the professional +astronomer the most convenient unit will be the light-year--that +is, the distance through which light would travel in one year. +This is equal to the product of 186,000 miles, the distance +travelled in one second, by 31,558,000, the number of seconds in a +year. The reader who chooses to do so may perform the +multiplication for himself. The product will amount to about +63,000 times the distance of the sun. + +[Illustration with caption: A Typical Star Cluster--Centauri] + +The nearest star whose distance we know, Alpha Centauri, is +distant from us more than four light-years. In all likelihood +this is really the nearest star, and it is not at all probable +that any other star lies within six light-years. Moreover, if we +were transported to this star the probability seems to be that the +sun would now be the nearest star to us. Flying to any other of +the stars whose parallax has been measured, we should probably +find that the average of the six or eight nearest stars around us +ranges somewhere between five and seven light-years. We may, in a +certain sense, call eight light-years a star-distance, meaning by +this term the average of the nearest distances from one star to +the surrounding ones. + +To put the result of measures of parallax into another form, let +us suppose, described around our sun as a centre, a system of +concentric spheres each of whose surfaces is at the distance of +six light-years outside the sphere next within it. The inner is at +the distance of six light-years around the sun. The surface of the +second sphere will be twelve light-years away, that of the third +eighteen, etc. The volumes of space within each of these spheres +will be as the cubes of the diameters. The most likely conclusion +we can draw from measures of parallax is that the first sphere +will contain, beside the sun at its centre, only Alpha Centauri. +The second, twelve light-years away, will probably contain, +besides these two, six other stars, making eight in all. The third +may contain twenty-one more, making twenty-seven stars within the +third sphere, which is the cube of three. Within the fourth would +probably be found sixty-four stars, this being the cube of four, +and so on. + +Beyond this no measures of parallax yet made will give us much +assistance. We can only infer that probably the same law holds for +a large number of spheres, though it is quite certain that it does +not hold indefinitely. For more light on the subject we must have +recourse to the proper motions. The latest words of astronomy on +this subject may be briefly summarized. As a rule, no star is at +rest. Each is moving through space with a speed which differs +greatly with different stars, but is nearly always swift, indeed, +when measured by any standard to which we are accustomed. Slow and +halting, indeed, is that star which does not make more than a mile +a second. With two or three exceptions, where the attraction of a +companion comes in, the motion of every star, so far as yet +determined, takes place in a straight line. In its outward motion +the flying body deviates neither to the right nor left. It is safe +to say that, if any deviation is to take place, thousands of years +will be required for our terrestrial observers to recognize it. + +Rapid as the course of these objects is, the distances which we +have described are such that, in the great majority of cases, all +the observations yet made on the positions of the stars fail to +show any well-established motion. It is only in the case of the +nearer of these objects that we can expect any motion to be +perceptible during the period, in no case exceeding one hundred +and fifty years, through which accurate observations extend. The +efforts of all the observatories which engage in such work are, up +to the present time, unequal to the task of grappling with the +motions of all the stars that can be seen with the instruments, +and reaching a decision as to the proper motion in each particular +case. As the question now stands, the aim of the astronomer is to +determine what stars have proper motions large enough to be well +established. To make our statement on this subject clear, it must +be understood that by this term the astronomer does not mean the +speed of a star in space, but its angular motion as he observes it +on the celestial sphere. A star moving forward with a given speed +will have a greater proper motion according as it is nearer to us. +To avoid all ambiguity, we shall use the term "speed" to express +the velocity in miles per second with which such a body moves +through space, and the term "proper motion" to express the +apparent angular motion which the astronomer measures upon the +celestial sphere. + +Up to the present time, two stars have been found whose proper +motions are so large that, if continued, the bodies would make a +complete circuit of the heavens in less than 200,000 years. One of +these would require about 160,000; the other about 180,000 years +for the circuit. Of other stars having a rapid motion only about +one hundred would complete their course in less than a million of +years. + +Quite recently a system of observations upon stars to the ninth +magnitude has been nearly carried through by an international +combination of observatories. The most important conclusion from +these observations relates to the distribution of the stars with +reference to the Milky Way, which we have already described. We +have shown that stars of every magnitude, bright and faint, show a +tendency to crowd towards this belt. It is, therefore, remarkable +that no such tendency is seen in the case of those stars which +have proper motions large enough to be accurately determined. So +far as yet appears, such stars are equally scattered over the +heavens, without reference to the course of the Milky Way. The +conclusion is obvious. These stars are all inside the girdle of +the Milky Way, and within the sphere which contains them the +distribution in space is approximately uniform. At least there is +no well-marked condensation in the direction of the galaxy nor any +marked thinning out towards its poles. What can we say as to the +extent of this sphere? + +To answer this question, we have to consider whether there is any +average or ordinary speed that a star has in space. A great number +of motions in the line of sight--that is to say, in the direction +of the line from us to the star--have been measured with great +precision by Campbell at the Lick Observatory, and by other +astronomers. The statistical investigations of Kaptoyn also throw +much light on the subject. The results of these investigators +agree well in showing an average speed in space--a straight-ahead +motion we may call it--of twenty-one miles per second. Some stars +may move more slowly than this to any extent; others more rapidly. +In two or three cases the speed exceeds one hundred miles per +second, but these are quite exceptional. By taking several +thousand stars having a given proper motion, we may form a general +idea of their average distance, though a great number of them will +exceed this average to a considerable extent. The conclusion drawn +in this way would be that the stars having an apparent proper +motion of 10" per century or more are mostly contained within, or +lie not far outside of a sphere whose surface is at a distance +from us of 200 light-years. Granting the volume of space which we +have shown that nature seems to allow to each star, this sphere +should contain 27,000 stars in all. There are about 10,000 stars +known to have so large a proper motion as 10". But there is no +actual discordance between these results, because not only are +there, in all probability, great numbers of stars of which the +proper motion is not yet recognized, but there are within the +sphere a great number of stars whose motion is less than the +average. On the other hand, it is probable that a considerable +number of the 10,000 stars lie at a distance at least one-half +greater than that of the radius of the sphere. + +On the whole, it seems likely that, out to a distance of 300 or +even 400 light-years, there is no marked inequality in star +distribution. If we should explore the heavens to this distance, +we should neither find the beginning of the Milky Way in one +direction nor a very marked thinning out in the other. This +conclusion is quite accordant with the probabilities of the case. +If all the stars which form the groundwork of the Milky Way should +be blotted out, we should probably find 100,000,000, perhaps even +more, remaining. Assigning to each star the space already shown to +be its quota, we should require a sphere of about 3000 light-years +radius to contain such a number of stars. At some such distance as +this, we might find a thinning out of the stars in the direction +of the galactic poles, or the commencement of the Milky Way in the +direction of this stream. + +Even if this were not found at the distance which we have +supposed, it is quite certain that, at some greater distance, we +should at least find that the region of the Milky Way is richer in +stars than the region near the galactic poles. There is strong +reason, based on the appearance of the stars of the Milky Way, +their physical constitution, and their magnitudes as seen in the +telescope, to believe that, were we placed on one of these stars, +we should find the stars around us to be more thickly strewn than +they are around our system. In other words, the quota of space +filled by each star is probably less in the region of the Milky +Way than it is near the centre where we seem to be situated. + +We are, therefore, presented with what seems to be the most +extraordinary spectacle that the universe can offer, a ring of +stars spanning it, and including within its limits by far the +great majority of the stars within our system. We have in this +spectacle another example of the unity which seems to pervade the +system. We might imagine the latter so arranged as to show +diversity to any extent. We might have agglomerations of stars +like those of the Milky Way situated in some corner of the system, +or at its centre, or scattered through it here and there in every +direction. But such is not the case. There are, indeed, a few +star-clusters scattered here and there through the system; but +they are essentially different from the clusters of the Milky Way, +and cannot be regarded as forming an important part of the general +plan. In the case of the galaxy we have no such scattering, but +find the stars built, as it were, into this enormous ring, having +similar characteristics throughout nearly its whole extent, and +having within it a nearly uniform scattering of stars, with here +and there some collected into clusters. Such, to our limited +vision, now appears the universe as a whole. + +We have already alluded to the conclusion that an absolutely +infinite system of stars would cause the entire heavens to be +filled with a blaze of light as bright as the sun. It is also true +that the attractive force within such a universe would be +infinitely great in some direction or another. But neither of +these considerations enables us to set a limit to the extent of +our system. In two remarkable papers by Lord Kelvin which have +recently appeared, the one being an address before the British +Association at its Glasgow meeting, in 1901, are given the results +of some numerical computations pertaining to this subject. +Granting that the stars are scattered promiscuously through space +with some approach to uniformity in thickness, and are of a known +degree of brilliancy, it is easy to compute how far out the system +must extend in order that, looking up at the sky, we shall see a +certain amount of light coming from the invisible stars. Granting +that, in the general average, each star is as bright as the sun, +and that their thickness is such that within a sphere of 3300 +light-years there are 1,000,000,000 stars, if we inquire how far +out such a system must be continued in order that the sky shall +shine with even four per cent of the light of the sun, we shall +find the distance of its boundary so great that millions of +millions of years would be required for the light of the outer +stars to reach the centre of the system. In view of the fact that +this duration in time far exceeds what seems to be the possible +life duration of a star, so far as our knowledge of it can extend, +the mere fact that the sky does not glow with any such brightness +proves little or nothing as to the extent of the system. + +We may, however, replace these purely negative considerations by +inquiring how much light we actually get from the invisible stars +of our system. Here we can make a definite statement. Mark out a +small circle in the sky 1 degree in diameter. The quantity of +light which we receive on a cloudless and moonless night from the +sky within this circle admits of actual determination. From the +measures so far available it would seem that, in the general +average, this quantity of light is not very different from that of +a star of the fifth magnitude. This is something very different +from a blaze of light. A star of the fifth magnitude is scarcely +more than plainly visible to ordinary vision. The area of the +whole sky is, in round numbers, about 50,000 times that of the +circle we have described. It follows that the total quantity of +light which we receive from all the stars is about equal to that +of 50,000 stars of the fifth magnitude--somewhat more than 1000 of +the first magnitude. This whole amount of light would have to be +multiplied by 90,000,000 to make a light equal to that of the sun. +It is, therefore, not at all necessary to consider how far the +system must extend in order that the heavens should blaze like the +sun. Adopting Lord Kelvin's hypothesis, we shall find that, in +order that we may receive from the stars the amount of light we +have designated, this system need not extend beyond some 5000 +light-years. But this hypothesis probably overestimates the +thickness of the stars in space. It does not seem probable that +there are as many as 1,000,000,000 stars within the sphere of 3300 +light-years. Nor is it at all certain that the light of the +average star is equal to that of the sun. It is impossible, in the +present state of our knowledge, to assign any definite value to +this average. To do so is a problem similar to that of assigning +an average weight to each component of the animal creation, from +the microscopic insects which destroy our plants up to the +elephant. What we can say with a fair approximation to confidence +is that, if we could fly out in any direction to a distance of +20,000, perhaps even of 10,000, light-years, we should find that +we had left a large fraction of our system behind us. We should +see its boundary in the direction in which we had travelled much +more certainly than we see it from our stand-point. + +We should not dismiss this branch of the subject without saying +that considerations are frequently adduced by eminent authorities +which tend to impair our confidence in almost any conclusion as to +the limits of the stellar system. The main argument is based on +the possibility that light is extinguished in its passage through +space; that beyond a certain distance we cannot see a star, +however bright, because its light is entirely lost before reaching +us. That there could be any loss of light in passing through an +absolute vacuum of any extent cannot be admitted by the physicist +of to-day without impairing what he considers the fundamental +principles of the vibration of light. But the possibility that the +celestial spaces are pervaded by matter which might obstruct the +passage of light is to be considered. We know that minute meteoric +particles are flying through our system in such numbers that the +earth encounters several millions of them every day, which appear +to us in the familiar phenomena of shooting-stars. If such +particles are scattered through all space, they must ultimately +obstruct the passage of light. We know little of the size of these +bodies, but, from the amount of energy contained in their light as +they are consumed in the passage through our atmosphere, it does +not seem at all likely that they are larger than grains of sand +or, perhaps, minute pebbles. They are probably vastly more +numerous in the vicinity of the sun than in the interstellar +spaces, since they would naturally tend to be collected by the +sun's attraction. In fact there are some reasons for believing +that most of these bodies are the debris of comets; and the latter +are now known to belong to the solar system, and not to the +universe at large. + +But whatever view we take of these possibilities, they cannot +invalidate our conclusion as to the general structure of the +stellar system as we know it. Were meteors so numerous as to cut +off a large fraction of the light from the more distant stars, we +should see no Milky Way, but the apparent thickness of the stars +in every direction would be nearly the same. The fact that so many +more of these objects are seen around the galactic belt than in +the direction of its poles shows that, whatever extinction light +may suffer in going through the greatest distances, we see nearly +all that comes from stars not more distant than the Milky Way +itself. + +Intimately connected with the subject we have discussed is the +question of the age of our system, if age it can be said to have. +In considering this question, the simplest hypothesis to suggest +itself is that the universe has existed forever in some such form +as we now see it; that it is a self-sustaining system, able to go +on forever with only such cycles of transformation as may repeat +themselves indefinitely, and may, therefore, have repeated +themselves indefinitely in the past. Ordinary observation does not +make anything known to us which would seem to invalidate this +hypothesis. In looking upon the operations of the universe, we may +liken ourselves to a visitor to the earth from another sphere who +has to draw conclusions about the life of an individual man from +observations extending through a few days. During that time, he +would see no reason why the life of the man should have either a +beginning or an end. He sees a daily round of change, activity and +rest, nutrition and waste; but, at the end of the round, the +individual is seemingly restored to his state of the day before. +Why may not this round have been going on forever, and continue in +the future without end? It would take a profounder course of +observation and a longer time to show that, notwithstanding this +seeming restoration, an imperceptible residual of vital energy, +necessary to the continuance of life, has not been restored, and +that the loss of this residuum day by day must finally result in +death. + +The case is much the same with the great bodies of the universe. +Although, to superficial observation, it might seem that they +could radiate their light forever, the modern generalizations of +physics show that such cannot be the case. The radiation of light +necessarily involves a corresponding loss of heat and with it the +expenditure of some form of energy. The amount of energy within +any body is necessarily limited. The supply must be exhausted +unless the energy of the light sent out into infinite space is, in +some way, restored to the body which expended it. The possibility +of such a restoration completely transcends our science. How can +the little vibration which strikes our eye from some distant star, +and which has been perhaps thousands of years in reaching us, find +its way back to its origin? The light emitted by the sun 10,000 +years ago is to-day pursuing its way in a sphere whose surface is +10,000 light-years distant on all sides. Science has nothing even +to suggest the possibility of its restoration, and the most +delicate observations fail to show any return from the +unfathomable abyss. + +Up to the time when radium was discovered, the most careful +investigations of all conceivable sources of supply had shown only +one which could possibly be of long duration. This is the +contraction which is produced in the great incandescent bodies of +the universe by the loss of the heat which they radiate. As +remarked in the preceding essay, the energy generated by the sun's +contraction could not have kept up its present supply of heat for +much more than twenty or thirty millions of years, while the study +of earth and ocean shows evidence of the action of a series of +causes which must have been going on for hundreds of millions of +years. + +The antagonism between the two conclusions is even more marked +than would appear from this statement. The period of the sun's +heat set by the astronomical physicist is that during which our +luminary could possibly have existed in its present form. The +period set by the geologist is not merely that of the sun's +existence, but that during which the causes effecting geological +changes have not undergone any complete revolution. If, at any +time, the sun radiated much less than its present amount of heat, +no water could have existed on the earth's surface except in the +form of ice; there would have been scarcely any evaporation, and +the geological changes due to erosion could not have taken place. +Moreover, the commencement of the geological operations of which +we speak is by no means the commencement of the earth's existence. +The theories of both parties agree that, for untold aeons before +the geological changes now visible commenced, our planet was a +molten mass, perhaps even an incandescent globe like the sun. +During all those aeons the sun must have been in existence as a +vast nebulous mass, first reaching as far as the earth's orbit, +and slowly contracting its dimensions. And these aeons are to be +included in any estimate of the age of the sun. + +The doctrine of cosmic evolution--the theory which in former times +was generally known as the nebular hypothesis--that the heavenly +bodies were formed by the slow contraction of heated nebulous +masses, is indicated by so many facts that it seems scarcely +possible to doubt it except on the theory that the laws of nature +were, at some former time, different from those which we now see +in operation. Granting the evolutionary hypothesis, every star has +its lifetime. We can even lay down the law by which it passes from +infancy to old age. All stars do not have the same length of life; +the rule is that the larger the star, or the greater the mass of +matter which composes it, the longer will it endure. Up to the +present time, science can do nothing more than point out these +indications of a beginning, and their inevitable consequence, that +there is to be an end to the light and heat of every heavenly +body. But no cautious thinker can treat such a subject with the +ease of ordinary demonstration. The investigator may even be +excused if he stands dumb with awe before the creation of his own +intellect. Our accurate records of the operations of nature extend +through only two or three centuries, and do not reach a +satisfactory standard until within a single century. The +experience of the individual is limited to a few years, and beyond +this period he must depend upon the records of his ancestors. All +his knowledge of the laws of nature is derived from this very +limited experience. How can he essay to describe what may have +been going on hundreds of millions of years in the past? Can he +dare to say that nature was the same then as now? + +It is a fundamental principle of the theory of evolution, as +developed by its greatest recent expounder, that matter itself is +eternal, and that all the changes which have taken place in the +universe, so far as made up of matter, are in the nature of +transformations of this eternal substance. But we doubt whether +any physical philosopher of the present day would be satisfied to +accept any demonstration of the eternity of matter. All he would +admit is that, so far as his observation goes, no change in the +quantity of matter can be produced by the action of any known +cause. It seems to be equally uncreatable and indestructible. But +he would, at the same time, admit that his experience no more +sufficed to settle the question than the observation of an animal +for a single day would settle the question of the duration of its +life, or prove that it had neither beginning nor end. He would +probably admit that even matter itself may be a product of +evolution. The astronomer finds it difficult to conceive that the +great nebulous masses which he sees in the celestial spaces-- +millions of times larger than the whole solar system, yet so +tenuous that they offer not the slightest obstruction to the +passage of a ray of light through their whole length--situated in +what seems to be a region of eternal cold, below anything that we +can produce on the earth's surface, yet radiating light, and with +it heat, like an incandescent body--can be made up of the same +kind of substance that we have around us on the earth's surface. +Who knows but that the radiant property that Becquerel has found +in certain forms of matter may be a residuum of some original form +of energy which is inherent in great cosmical masses, and has fed +our sun during all the ages required by the geologist for the +structure of the earth's crusts? It may be that in this phenomenon +we have the key to the great riddle of the universe, with which +profounder secrets of matter than any we have penetrated will be +opened to the eyes of our successors. + + + + + +IV + +THE EXTENT OF THE UNIVERSE + + +We cannot expect that the wisest men of our remotest posterity, +who can base their conclusions upon thousands of years of accurate +observation, will reach a decision on this subject without some +measure of reserve. Such being the case, it might appear the +dictate of wisdom to leave its consideration to some future age, +when it may be taken up with better means of information than we +now possess. But the question is one which will refuse to be +postponed so long as the propensity to think of the possibilities +of creation is characteristic of our race. The issue is not +whether we shall ignore the question altogether, like Eve in the +presence of Raphael; but whether in studying it we shall confine +our speculations within the limits set by sound scientific +reasoning. Essaying to do this, I invite the reader's attention to +what science may suggest, admitting in advance that the sphere of +exact knowledge is small compared with the possibilities of +creation, and that outside this sphere we can state only more or +less probable conclusions. + +The reader who desires to approach this subject in the most +receptive spirit should begin his study by betaking himself on a +clear, moonless evening, when he has no earthly concern to disturb +the serenity of his thoughts, to some point where he can lie on +his back on bench or roof, and scan the whole vault of heaven at +one view. He can do this with the greatest pleasure and profit in +late summer or autumn--winter would do equally well were it +possible for the mind to rise so far above bodily conditions that +the question of temperature should not enter. The thinking man who +does this under circumstances most favorable for calm thought will +form a new conception of the wonder of the universe. If summer or +autumn be chosen, the stupendous arch of the Milky Way will pass +near the zenith, and the constellation Lyra, led by its beautiful +blue Vega of the first magnitude, may be not very far from that +point. South of it will be seen the constellation Aquila, marked +by the bright Altair, between two smaller but conspicuous stars. +The bright Arcturus will be somewhere in the west, and, if the +observation is not made too early in the season, Aldebaran will be +seen somewhere in the east. When attention is concentrated on the +scene the thousands of stars on each side of the Milky Way will +fill the mind with the consciousness of a stupendous and all- +embracing frame, beside which all human affairs sink into +insignificance. A new idea will be formed of such a well-known +fact of astronomy as the motion of the solar system in space, by +reflecting that, during all human history, the sun, carrying the +earth with it, has been flying towards a region in or just south +of the constellation Lyra, with a speed beyond all that art can +produce on earth, without producing any change apparent to +ordinary vision in the aspect of the constellation. Not only Lyra +and Aquila, but every one of the thousand stars which form the +framework of the sky, were seen by our earliest ancestors just as +we see them now. Bodily rest may be obtained at any time by +ceasing from our labors, and weary systems may find nerve rest at +any summer resort; but I know of no way in which complete rest can +be obtained for the weary soul--in which the mind can be so +entirely relieved of the burden of all human anxiety--as by the +contemplation of the spectacle presented by the starry heavens +under the conditions just described. As we make a feeble attempt +to learn what science can tell us about the structure of this +starry frame, I hope the reader will allow me to at least fancy +him contemplating it in this way. + +The first question which may suggest itself to the inquiring +reader is: How is it possible by any methods of observation yet +known to the astronomer to learn anything about the universe as a +whole? We may commence by answering this question in a somewhat +comprehensive way. It is possible only because the universe, vast +though it is, shows certain characteristics of a unified and +bounded whole. It is not a chaos, it is not even a collection of +things, each of which came into existence in its own separate way. +If it were, there would be nothing in common between two widely +separate regions of the universe. But, as a matter of fact, +science shows unity in the whole structure, and diversity only in +details. The Milky Way itself will be seen by the most ordinary +observer to form a single structure. This structure is, in some +sort, the foundation on which the universe is built. It is a +girdle which seems to span the whole of creation, so far as our +telescopes have yet enabled us to determine what creation is; and +yet it has elements of similarity in all its parts. What has yet +more significance, it is in some respects unlike those parts of +the universe which lie without it, and even unlike those which lie +in that central region within it where our system is now situated. +The minute stars, individually far beyond the limit of visibility +to the naked eye, which form its cloudlike agglomerations, are +found to be mostly bluer in color, from one extreme to the other, +than the general average of the stars which make up the rest of +the universe. + +In the preceding essay on the structure of the universe, we have +pointed out several features of the universe showing the unity of +the whole. We shall now bring together these and other features +with a view of showing their relation to the question of the +extent of the universe. + +The Milky Way being in a certain sense the foundation on which the +whole system is constructed, we have first to notice the symmetry +of the whole. This is seen in the fact that a certain resemblance +is found in any two opposite regions of the sky, no matter where +we choose them. If we take them in the Milky Way, the stars are +more numerous than elsewhere; if we take opposite regions in or +near the Milky Way, we shall find more stars in both of them than +elsewhere; if we take them in the region anywhere around the poles +of the Milky Way, we shall find fewer stars, but they will be +equally numerous in each of the two regions. We infer from this +that whatever cause determined the number of the stars in space +was of the same nature in every two antipodal regions of the +heavens. + +Another unity marked with yet more precision is seen in the +chemical elements of which stars are composed. We know that the +sun is composed of the same elements which we find on the earth +and into which we resolve compounds in our laboratories. These +same elements are found in the most distant stars. It is true that +some of these bodies seem to contain elements which we do not find +on earth. But as these unknown elements are scattered from one +extreme of the universe to the other, they only serve still +further to enforce the unity which runs through the whole. The +nebulae are composed, in part at least, of forms of matter +dissimilar to any with which we are acquainted. But, different +though they may be, they are alike in their general character +throughout the whole field we are considering. Even in such a +feature as the proper motions of the stars, the same unity is +seen. The reader doubtless knows that each of these objects is +flying through space on its own course with a speed comparable +with that of the earth around the sun. These speeds range from the +smallest limit up to more than one hundred miles a second. Such +diversity might seem to detract from the unity of the whole; but +when we seek to learn something definite by taking their average, +we find this average to be, so far as can yet be determined, much +the same in opposite regions of the universe. Quite recently it +has become probable that a certain class of very bright stars +known as Orion stars--because there are many of them in the most +brilliant of our constellations--which are scattered along the +whole course of the Milky Way, have one and all, in the general +average, slower motions than other stars. Here again we have a +definable characteristic extending through the universe. In +drawing attention to these points of similarity throughout the +whole universe, it must not be supposed that we base our +conclusions directly upon them. The point they bring out is that +the universe is in the nature of an organized system; and it is +upon the fact of its being such a system that we are able, by +other facts, to reach conclusions as to its structure, extent, and +other characteristics. + +One of the great problems connected with the universe is that of +its possible extent. How far away are the stars? One of the +unities which we have described leads at once to the conclusion +that the stars must be at very different distances from us; +probably the more distant ones are a thousand times as far as the +nearest; possibly even farther than this. This conclusion may, in +the first place, be based on the fact that the stars seem to be +scattered equally throughout those regions of the universe which +are not connected with the Milky Way. To illustrate the principle, +suppose a farmer to sow a wheat-field of entirely unknown extent +with ten bushels of wheat. We visit the field and wish to have +some idea of its acreage. We may do this if we know how many +grains of wheat there are in the ten bushels. Then we examine a +space two or three feet square in any part of the field and count +the number of grains in that space. If the wheat is equally +scattered over the whole field, we find its extent by the simple +rule that the size of the field bears the same proportion to the +size of the space in which the count was made that the whole +number of grains in the ten bushels sown bears to the number of +grains counted. If we find ten grains in a square foot, we know +that the number of square feet in the whole field is one-tenth +that of the number of grains sown. So it is with the universe of +stars. If the latter are sown equally through space, the extent of +the space occupied must be proportional to the number of stars +which it contains. + +But this consideration does not tell us anything about the actual +distance of the stars or how thickly they may be scattered. To do +this we must be able to determine the distance of a certain number +of stars, just as we suppose the farmer to count the grains in a +certain small extent of his wheat-field. There is only one way in +which we can make a definite measure of the distance of any one +star. As the earth swings through its vast annual circuit round +the sun, the direction of the stars must appear to be a little +different when seen from one extremity of the circuit than when +seen from the other. This difference is called the parallax of the +stars; and the problem of measuring it is one of the most delicate +and difficult in the whole field of practical astronomy. + +The nineteenth century was well on its way before the instruments +of the astronomer were brought to such perfection as to admit of +the measurement. From the time of Copernicus to that of Bessel +many attempts had been made to measure the parallax of the stars, +and more than once had some eager astronomer thought himself +successful. But subsequent investigation always showed that he had +been mistaken, and that what he thought was the effect of parallax +was due to some other cause, perhaps the imperfections of his +instrument, perhaps the effect of heat and cold upon it or upon +the atmosphere through which he was obliged to observe the star, +or upon the going of his clock. Thus things went on until 1837, +when Bessel announced that measures with a heliometer--the most +refined instrument that has ever been used in measurement--showed +that a certain star in the constellation Cygnus had a parallax of +one-third of a second. It may be interesting to give an idea of +this quantity. Suppose one's self in a house on top of a mountain +looking out of a window one foot square, at a house on another +mountain one hundred miles away. One is allowed to look at that +distant house through one edge of the pane of glass and then +through the opposite edge; and he has to determine the change in +the direction of the distant house produced by this change of one +foot in his own position. From this he is to estimate how far off +the other mountain is. To do this, one would have to measure just +about the amount of parallax that Bessel found in his star. And +yet this star is among the few nearest to our system. The nearest +star of all, Alpha Centauri, visible only in latitudes south of +our middle ones, is perhaps half as far as Bessel's star, while +Sirius and one or two others are nearly at the same distance. +About 100 stars, all told, have had their parallax measured with a +greater or less degree of probability. The work is going on from +year to year, each successive astronomer who takes it up being +able, as a general rule, to avail himself of better instruments or +to use a better method. But, after all, the distances of even some +of the 100 stars carefully measured must still remain quite +doubtful. + +Let us now return to the idea of dividing the space in which the +universe is situated into concentric spheres drawn at various +distances around our system as a centre. Here we shall take as our +standard a distance 400,000 times that of the sun from the earth. +Regarding this as a unit, we imagine ourselves to measure out in +any direction a distance twice as great as this--then another +equal distance, making one three times as great, and so +indefinitely. We then have successive spheres of which we take the +nearer one as the unit. The total space filled by the second +sphere will be 8 times the unit; that of the third space 27 times, +and so on, as the cube of each distance. Since each sphere +includes all those within it, the volume of space between each two +spheres will be proportional to the difference of these numbers-- +that is, to 1, 7, 19, etc. Comparing these volumes with the number +of stars probably within them, the general result up to the +present time is that the number of stars in any of these spheres +will be about equal to the units of volume which they comprise, +when we take for this unit the smallest and innermost of the +spheres, having a radius 400,000 times the sun's distance. We are +thus enabled to form some general idea of how thickly the stars +are sown through space. We cannot claim any numerical exactness +for this idea, but in the absence of better methods it does afford +us some basis for reasoning. + +Now we can carry on our computation as we supposed the farmer to +measure the extent of his wheat-field. Let us suppose that there +are 125,000,000 stars in the heavens. This is an exceedingly rough +estimate, but let us make the supposition for the time being. +Accepting the view that they are nearly equally scattered +throughout space, it will follow that they must be contained +within a volume equal to 125,000,000 times the sphere we have +taken as our unit. We find the distance of the surface of this +sphere by extracting the cube root of this number, which gives us +500. We may, therefore, say, as the result of a very rough +estimate, that the number of stars we have supposed would be +contained within a distance found by multiplying 400,000 times the +distance of the sun by 500; that is, that they are contained +within a region whose boundary is 200,000,000 times the distance +of the sun. This is a distance through which light would travel in +about 3300 years. + +It is not impossible that the number of stars is much greater than +that we have supposed. Let us grant that there are eight times as +many, or 1,000,000,000. Then we should have to extend the boundary +of our universe twice as far, carrying it to a distance which +light would require 6600 years to travel. + +There is another method of estimating the thickness with which +stars are sown through space, and hence the extent of the +universe, the result of which will be of interest. It is based on +the proper motion of the stars. One of the greatest triumphs of +astronomy of our time has been the measurement of the actual speed +at which many of the stars are moving to or from us in space. +These measures are made with the spectroscope. Unfortunately, they +can be best made only on the brighter stars--becoming very +difficult in the case of stars not plainly visible to the naked +eye. Still the motions of several hundreds have been measured and +the number is constantly increasing. + +A general result of all these measures and of other estimates may +be summed up by saying that there is a certain average speed with +which the individual stars move in space; and that this average is +about twenty miles per second. We are also able to form an +estimate as to what proportion of the stars move with each rate of +speed from the lowest up to a limit which is probably as high as +150 miles per second. Knowing these proportions we have, by +observation of the proper motions of the stars, another method of +estimating how thickly they are scattered in space; in other +words, what is the volume of space which, on the average, contains +a single star. This method gives a thickness of the stars greater +by about twenty-five per cent, than that derived from the measures +of parallax. That is to say, a sphere like the second we have +proposed, having a radius 800,000 times the distance of the sun, +and therefore a diameter 1,600,000 times this distance, would, +judging by the proper motions, have ten or twelve stars contained +within it, while the measures of parallax only show eight stars +within the sphere of this diameter having the sun as its centre. +The probabilities are in favor of the result giving the greater +thickness of the stars. But, after all, the discrepancy does not +change the general conclusion as to the limits of the visible +universe. If we cannot estimate its extent with the same certainty +that we can determine the size of the earth, we can still form a +general idea of it. + +The estimates we have made are based on the supposition that the +stars are equally scattered in space. We have good reason to +believe that this is true of all the stars except those of the +Milky Way. But, after all, the latter probably includes half the +whole number of stars visible with a telescope, and the question +may arise whether our results are seriously wrong from this cause. +This question can best be solved by yet another method of +estimating the average distance of certain classes of stars. + +The parallaxes of which we have heretofore spoken consist in the +change in the direction of a star produced by the swing of the +earth from one side of its orbit to the other. But we have already +remarked that our solar system, with the earth as one of its +bodies, has been journeying straightforward through space during +all historic times. It follows, therefore, that we are continually +changing the position from which we view the stars, and that, if +the latter were at rest, we could, by measuring the apparent speed +with which they are moving in the opposite direction from that of +the earth, determine their distance. But since every star has its +own motion, it is impossible, in any one case, to determine how +much of the apparent motion is due to the star itself, and how +much to the motion of the solar system through space. Yet, by +taking general averages among groups of stars, most of which are +probably near each other, it is possible to estimate the average +distance by this method. When an attempt is made to apply it, so +as to obtain a definite result, the astronomer finds that the data +now available for the purpose are very deficient. The proper +motion of a star can be determined only by comparing its observed +position in the heavens at two widely separate epochs. +Observations of sufficient precision for this purpose were +commenced about 1750 at the Greenwich Observatory, by Bradley, +then Astronomer Royal of England. But out of 3000 stars which he +determined, only a few are available for the purpose. Even since +his time, the determinations made by each generation of +astronomers have not been sufficiently complete and systematic to +furnish the material for anything like a precise determination of +the proper motions of stars. To determine a single position of any +one star involves a good deal of computation, and if we reflect +that, in order to attack the problem in question in a satisfactory +way, we should have observations of 1,000,000 of these bodies made +at intervals of at least a considerable fraction of a century, we +see what an enormous task the astronomers dealing with this +problem have before them, and how imperfect must be any +determination of the distance of the stars based on our motion +through space. So far as an estimate can be made, it seems to +agree fairly well with the results obtained by the other methods. +Speaking roughly, we have reason, from the data so far available, +to believe that the stars of the Milky Way are situated at a +distance between 100,000,000 and 200,000,000 times the distance of +the sun. At distances less than this it seems likely that the +stars are distributed through space with some approach to +uniformity. We may state as a general conclusion, indicated by +several methods of making the estimate, that nearly all the stars +which we can see with our telescopes are contained within a sphere +not likely to be much more than 200,000,000 times the distance of +the sun. + +The inquiring reader may here ask another question. Granting that +all the stars we can see are contained within this limit, may +there not be any number of stars outside the limit which are +invisible only because they are too far away to be seen? + +This question may be answered quite definitely if we grant that +light from the most distant stars meets with no obstruction in +reaching us. The most conclusive answer is afforded by the measure +of starlight. If the stars extended out indefinitely, then the +number of those of each order of magnitude would be nearly four +times that of the magnitude next brighter. For example, we should +have nearly four times as many stars of the sixth magnitude as of +the fifth; nearly four times as many of the seventh as of the +sixth, and so on indefinitely. Now, it is actually found that +while this ratio of increase is true for the brighter stars, it is +not so for the fainter ones, and that the increase in the number +of the latter rapidly falls off when we make counts of the fainter +telescopic stars. In fact, it has long been known that, were the +universe infinite in extent, and the stars equally scattered +through all space, the whole heavens would blaze with the light of +countless millions of distant stars separately invisible even with +the telescope. + +The only way in which this conclusion can be invalidated is by the +possibility that the light of the stars is in some way +extinguished or obstructed in its passage through space. A theory +to this effect was propounded by Struve nearly a century ago, but +it has since been found that the facts as he set them forth do not +justify the conclusion, which was, in fact, rather hypothetical. +The theories of modern science converge towards the view that, in +the pure ether of space, no single ray of light can ever be lost, +no matter how far it may travel. But there is another possible +cause for the extinction of light. During the last few years +discoveries of dark and therefore invisible stars have been made +by means of the spectroscope with a success which would have been +quite incredible a very few years ago, and which, even to-day, +must excite wonder and admiration. The general conclusion is that, +besides the shining stars which exist in space, there may be any +number of dark ones, forever invisible in our telescopes. May it +not be that these bodies are so numerous as to cut off the light +which we would otherwise receive from the more distant bodies of +the universe? It is, of course, impossible to answer this question +in a positive way, but the probable conclusion is a negative one. +We may say with certainty that dark stars are not so numerous as +to cut off any important part of the light from the stars of the +Milky Way, because, if they did, the latter would not be so +clearly seen as it is. Since we have reason to believe that the +Milky Way comprises the more distant stars of our system, we may +feel fairly confident that not much light can be cut off by dark +bodies from the most distant region to which our telescopes can +penetrate. Up to this distance we see the stars just as they are. +Even within the limit of the universe as we understand it, it is +likely that more than one-half the stars which actually exist are +too faint to be seen by human vision, even when armed with the +most powerful telescopes. But their invisibility is due only to +their distance and the faintness of their intrinsic light, and not +to any obstructing agency. + +The possibility of dark stars, therefore, does not invalidate the +general conclusions at which our survey of the subject points. The +universe, so far as we can see it, is a bounded whole. It is +surrounded by an immense girdle of stars, which, to our vision, +appears as the Milky Way. While we cannot set exact limits to its +distance, we may yet confidently say that it is bounded. It has +uniformities running through its vast extent. Could we fly out to +distances equal to that of the Milky Way, we should find +comparatively few stars beyond the limits of that girdle. It is +true that we cannot set any definite limit and say that beyond +this nothing exists. What we can say is that the region containing +the visible stars has some approximation to a boundary. We may +fairly anticipate that each successive generation of astronomers, +through coming centuries, will obtain a little more light on the +subject--will be enabled to make more definite the boundaries of +our system of stars, and to draw more and more probable +conclusions as to the existence or non-existence of any object +outside of it. The wise investigator of to-day will leave to them +the task of putting the problem into a more positive shape. + + + + + +V + +MAKING AND USING A TELESCOPE + + +The impression is quite common that satisfactory views of the +heavenly bodies can be obtained only with very large telescopes, +and that the owner of a small one must stand at a great +disadvantage alongside of the fortunate possessor of a great one. +This is not true to the extent commonly supposed. Sir William +Herschel would have been delighted to view the moon through what +we should now consider a very modest instrument; and there are +some objects, especially the moon, which commonly present a more +pleasing aspect through a small telescope than through a large +one. The numerous owners of small telescopes throughout the +country might find their instruments much more interesting than +they do if they only knew what objects were best suited to +examination with the means at their command. There are many +others, not possessors of telescopes, who would like to know how +one can be acquired, and to whom hints in this direction will be +valuable. We shall therefore give such information as we are able +respecting the construction of a telescope, and the more +interesting celestial objects to which it may be applied. + +Whether the reader does or does not feel competent to undertake +the making of a telescope, it may be of interest to him to know +how it is done. First, as to the general principles involved, it +is generally known that the really vital parts of the telescope, +which by their combined action perform the office of magnifying +the object looked at, are two in number, the OBJECTIVE and the +EYE-PIECE. The former brings the rays of light which emanate from +the object to the focus where the image of the object is formed. +The eye-piece enables the observer to see this image to the best +advantage. + +The functions of the objective as well as those of the eye-piece +may, to a certain extent, each be performed by a single lens. +Galileo and his contemporaries made their telescopes in this way, +because they knew of no way in which two lenses could be made to +do better than one. But every one who has studied optics knows +that white light passing through a single lens is not all brought +to the same focus, but that the blue light will come to a focus +nearer the objective than the red light. There will, in fact, be a +succession of images, blue, green, yellow, and red, corresponding +to the colors of the spectrum. It is impossible to see these +different images clearly at the same time, because each of them +will render all the others indistinct. + +The achromatic object-glass, invented by Dollond, about 1750, +obviates this difficulty, and brings all the rays to nearly the +same focus. Nearly every one interested in the subject is aware +that this object-glass is composed of two lenses--a concave one of +flint-glass and a convex one of crown-glass, the latter being on +the side towards the object. This is the one vital part of the +telescope, the construction of which involves the greatest +difficulty. Once in possession of a perfect object-glass, the rest +of the telescope is a matter of little more than constructive +skill which there is no difficulty in commanding. + +The construction of the object-glass requires two completely +distinct processes: the making of the rough glass, which is the +work of the glass-maker; and the grinding and polishing into +shape, which is the work of the optician. The ordinary glass of +commerce will not answer the purpose of the telescope at all, +because it is not sufficiently clear and homogeneous. OPTICAL +GLASS, as it is called, must be made of materials selected and +purified with the greatest care, and worked in a more elaborate +manner than is necessary in any other kind of glass. In the time +of Dollond it was found scarcely possible to make good disks of +flint-glass more than three or four inches in diameter. Early in +the present century, Guinand, of Switzerland, invented a process +by which disks of much larger size could be produced. In +conjunction with the celebrated Fraunhofer he made disks of nine +or ten inches in diameter, which were employed by his colaborer in +constructing the telescopes which were so famous in their time. He +was long supposed to be in possession of some secret method of +avoiding the difficulties which his predecessors had met. It is +now believed that this secret, if one it was, consisted +principally in the constant stirring of the molten glass during +the process of manufacture. However this may be, it is a curious +historical fact that the most successful makers of these great +disks of glass have either been of the family of Guinand, or +successors, in the management of the family firm. It was Feil, a +son-in-law or near relative, who made the glass from which Clark +fabricated the lenses of the great telescope of the Lick +Observatory. His successor, Mantois, of Paris, carried the art to +a point of perfection never before approached. The transparency +and uniformity of his disks as well as the great size to which he +was able to carry them would suggest that he and his successors +have out-distanced all competitors in the process. He it was who +made the great 40-inch lens for the Yerkes Observatory. + +As optical glass is now made, the material is constantly stirred +with an iron rod during all the time it is melting in the furnace, +and after it has begun to cool, until it becomes so stiff that the +stirring has to cease. It is then placed, pot and all, in the +annealing furnace, where it is kept nearly at a melting heat for +three weeks or more, according to the size of the pot. When the +furnace has cooled off, the glass is taken out, and the pot is +broken from around it, leaving only the central mass of glass. +Having such a mass, there is no trouble in breaking it up into +pieces of all desirable purity, and sufficiently large for +moderate-sized telescopes. But when a great telescope of two feet +aperture or upward is to be constructed, very delicate and +laborious operations have to be undertaken. The outside of the +glass has first to be chipped off, because it is filled with +impurities from the material of the pot itself. But this is not +all. Veins of unequal density are always found extending through +the interior of the mass, no way of avoiding them having yet been +discovered. They are supposed to arise from the materials of the +pot and stirring rod, which become mixed in with the glass in +consequence of the intense heat to which all are subjected. These +veins must, so far as possible, be ground or chipped out with the +greatest care. The glass is then melted again, pressed into a flat +disk, and once more put into the annealing oven. In fact, the +operation of annealing must be repeated every time the glass is +melted. When cooled, it is again examined for veins, of which +great numbers are sure to be found. The problem now is to remove +these by cutting and grinding without either breaking the glass in +two or cutting a hole through it. If the parts of the glass are +once separated, they can never be joined without producing a bad +scar at the point of junction. So long, however, as the surface is +unbroken, the interior parts of the glass can be changed in form +to any extent. Having ground out the veins as far as possible, the +glass is to be again melted, and moulded into proper shape. In +this mould great care must be taken to have no folding of the +surface. Imagining the latter to be a sort of skin enclosing the +melted glass inside, it must be raised up wherever the glass is +thinnest, and the latter allowed to slowly run together beneath +it. + +[Illustration with caption: THE GLASS DISK.] + +If the disk is of flint, all the veins must be ground out on the +first or second trial, because after two or three mouldings the +glass will lose its transparency. A crown disk may, however, be +melted a number of times without serious injury. In many cases-- +perhaps the majority--the artisan finds that after all his months +of labor he cannot perfectly clear his glass of the noxious veins, +and he has to break it up into smaller pieces. When he finally +succeeds, the disk has the form of a thin grindstone two feet or +upward in diameter, according to the size of the telescope to be +made, and from two to three inches in thickness. The glass is then +ready for the optician. + +[Illustration with caption: THE OPTICIAN'S TOOL.] + +The first process to be performed by the optician is to grind the +glass into the shape of a lens with perfectly spherical surfaces. +The convex surface must be ground in a saucer-shaped tool of +corresponding form. It is impossible to make a tool perfectly +spherical in the first place, but success may be secured on the +geometrical principle that two surfaces cannot fit each other in +all positions unless both are perfectly spherical. The tool of the +optician is a very simple affair, being nothing more than a plate +of iron somewhat larger, perhaps a fourth, than the lens to be +ground to the corresponding curvature. In order to insure its +changing to fit the glass, it is covered on the interior with a +coating of pitch from an eighth to a quarter of an inch thick. +This material is admirably adapted to the purpose because it gives +way certainly, though very slowly, to the pressure of the glass. +In order that it may have room to change its form, grooves are cut +through it in both directions, so as to leave it in the form of +squares, like those on a chess-board. + +[Illustration with caption: THE OPTICIAN'S TOOL.] + +It is then sprinkled over with rouge, moistened with water, and +gently warmed. The roughly ground lens is then placed upon it, and +moved from side to side. The direction of the motion is slightly +changed with every stroke, so that after a dozen or so of strokes +the lines of motion will lie in every direction on the tool. This +change of direction is most readily and easily effected by the +operator slowly walking around as he polishes, at the same time +the lens is to be slowly turned around either in the opposite +direction or more rapidly yet in the same direction, so that the +strokes of the polisher shall cross the lens in all directions. +This double motion insures every part of the lens coming into +contact with every part of the polisher, and moving over it in +every direction. + +Then whatever parts either of the lens or of the polisher may be +too high to form a spherical surface will be gradually worn down, +thus securing the perfect sphericity of both. + +[Illustration with caption: GRINDING A LARGE LENS.] + +When the polishing is done by machinery, which is the custom in +Europe, with large lenses, the polisher is slid back and forth +over the lens by means of a crank attached to a revolving wheel. +The polisher is at the same time slowly revolving around a pivot +at its centre, which pivot the crank works into, and the glass +below it is slowly turned in an opposite direction. Thus the same +effect is produced as in the other system. Those who practice this +method claim that by thus using machinery the conditions of a +uniform polish for every part of the surface can be more perfectly +fulfilled than by a hand motion. The results, however, do not +support this view. No European optician will claim to do better +than the American firm of Alvan Clark & Sons in producing +uniformly good object-glasses, and this firm always does the work +by hand, moving the glass over the polisher, and not the polisher +over the glass. + +Having brought both flint and crown glasses into proper figure by +this process, they are joined together, and tested by observations +either upon a star in the heavens, or some illuminated point at a +little distance on the ground. The reflection of the sun from a +drop of quicksilver, a thermometer bulb, or even a piece of broken +bottle, makes an excellent artificial star. The very best optician +will always find that on a first trial his glass is not perfect. +He will find that he has not given exactly the proper curves to +secure achromatism. He must then change the figure of one or both +the glasses by polishing it upon a tool of slightly different +curvature. He may also find that there is some spherical +aberration outstanding. He must then alter his curve so as to +correct this. The correction of these little imperfections in the +figures of the lenses so as to secure perfect vision through them +is the most difficult branch of the art of the optician, and upon +his skill in practising it will depend more than upon anything +else his ultimate success and reputation. The shaping of a pair of +lenses in the way we have described is not beyond the power of any +person of ordinary mechanical ingenuity, possessing the necessary +delicacy of touch and appreciation of the problem he is attacking. +But to make a perfect objective of considerable size, which shall +satisfy all the wants of the astronomer, is an undertaking +requiring such accuracy of eyesight, and judgment in determining +where the error lies, and such skill in manipulating so as to +remove the defects, that the successful men in any one generation +can be counted on one's fingers. + +In order that the telescope may finally perform satisfactorily it +is not sufficient that the lenses should both be of proper figure; +they must also both be properly centred in their cells. If either +lens is tipped aside, or slid out from its proper central line, +the definition will be injured. As this is liable to happen with +almost any telescope, we shall explain how the proper adjustment +is to be made. + +The easiest way to test this adjustment is to set the cell with +the two glasses of the objective in it against a wall at night, +and going to a short distance, observe the reflection in the glass +of the flame of a candle held in the hand. Three or four +reflections will be seen from the different surfaces. The +observer, holding the candle before his eye, and having his line +of sight as close as possible to the flame, must then move until +the different images of the flame coincide with each other. If he +cannot bring them into coincidence, owing to different pairs +coinciding on different sides of the flame, the glasses are not +perfectly centred upon each other. When the centring is perfect, +the observer having the light in the line of the axes of the +lenses, and (if it were possible to do so) looking through the +centre of the flame, would see the three or four images all in +coincidence. As he cannot see through the flame itself, he must +look first on one side and then on the other, and see if the +arrangement of the images seen in the lenses is symmetrical. If, +going to different distances, he finds no deviation from symmetry, +in this respect the adjustment is near enough for all practical +purposes. + +A more artistic instrument than a simple candle is a small concave +reflector pierced through its centre, such as is used by +physicians in examining the throat. + +[Illustration with caption: IMAGE OF CANDLE-FLAME IN OBJECT- +GLASS.] + +[Illustration with caption: TESTING ADJUSTMENT OF OBJECT-GLASS.] + +Place this reflector in the prolongation of the optical axis, set +the candle so that the light from the reflector shall be shown +through the glass, and look through the opening. Images of the +reflector itself will then be seen in the object-glass, and if the +adjustment is perfect, the reflector can be moved so that they +will all come into coincidence together. + +When the objective is in the tube of the telescope, it is always +well to examine this adjustment from time to time, holding the +candle so that its light shall shine through the opening +perpendicularly upon the object-glass. The observer looks upon one +side of the flame, and then upon the other, to see if the images +are symmetrical in the different positions. If in order to see +them in this way the candle has to be moved to one side of the +central line of the tube, the whole objective must be adjusted. If +two images coincide in one position of the candle-flame, and two +in another position, so that they cannot all be brought together +in any position, it shows that the glasses are not properly +adjusted in their cell. It may be remarked that this last +adjustment is the proper work of the optician, since it is so +difficult that the user of the telescope cannot ordinarily effect +it. But the perpendicularity of the whole objective to the tube of +the telescope is liable to be deranged in use, and every one who +uses such an instrument should be able to rectify an error of this +kind. + +The question may be asked, How much of a telescope can an amateur +observer, under any circumstances, make for himself? As a general +rule, his work in this direction must be confined to the tube and +the mounting. We should not, it is true, dare to assert that any +ingenious young man, with a clear appreciation of optical +principles, could not soon learn to grind and polish an object- +glass for himself by the method we have described, and thus obtain +a much better instrument than Galileo ever had at his command. But +it would be a wonderful success if his home-made telescope was +equal to the most indifferent one which can be bought at an +optician's. The objective, complete in itself, can be purchased at +prices depending upon the size. + +[Footnote: The following is a rough rule for getting an idea of +the price of an achromatic objective, made to order, of the finest +quality. Take the cube of the diameter in inches, or, which is the +same thing, calculate the contents of a cubical box which would +hold a sphere of the same diameter as the clear aperture of the +glass. The price of the glass will then range from $1 to $1.75 for +each cubic inch in this box. For example, the price of a four-inch +objective will probably range from $64 to $112. Very small object- +glasses of one or two inches may be a little higher than would be +given by this rule. Instruments which are not first-class, but +will answer most of the purposes of the amateur, are much +cheaper.] + +[Illustration with caption: A VERY PRIMITIVE MOUNTING FOR A +TELESCOPE.] + +The tube for the telescope may be made of paper, by pasting a +great number of thicknesses around a long wooden cylinder. A yet +better tube is made of a simple wooden box. The best material, +however, is metal, because wood and pasteboard are liable both to +get out of shape, and to swell under the influence of moisture. +Tin, if it be of sufficient thickness, would be a very good +material. The brighter it is kept, the better. The work of fitting +the objective into one end of a tin tube of double thickness, and +properly adjusting it, will probably be quite within the powers of +the ordinary amateur. The fitting of the eye-piece into the other +end of the tube will require some skill and care both on his own +part and that of his tinsmith. + +Although the construction of the eye-piece is much easier than +that of the objective, since the same accuracy in adjusting the +curves is not necessary, yet the price is lower in a yet greater +degree, so that the amateur will find it better to buy than to +make his eye-piece, unless he is anxious to test his mechanical +powers. For a telescope which has no micrometer, the Huyghenian or +negative eye-piece, as it is commonly called, is the best. As made +by Huyghens, it consists of two plano-convex lenses, with their +plane sides next the eye, as shown in the figure. + +[Illustration with caption: THE HUYGHENIAN EYE-PIECE.] + +So far as we have yet described our telescope it is optically +complete. If it could be used as a spy-glass by simply holding it +in the hand, and pointing at the object we wish to observe, there +would be little need of any very elaborate support. But if a +telescope, even of the smallest size, is to be used with +regularity, a proper "mounting" is as essential as a good +instrument. Persons unpractised in the use of such instruments are +very apt to underrate the importance of those accessories which +merely enable us to point the telescope. An idea of what is wanted +in the mounting may readily be formed if the reader will try to +look at a star with an ordinary good-sized spy-glass held in the +hand, and then imagine the difficulties he meets with multiplied +by fifty. + +The smaller and cheaper telescopes, as commonly sold, are mounted +on a simple little stand, on which the instrument admits of a +horizontal and vertical motion. If one only wants to get a few +glimpses of a celestial object, this mounting will answer his +purpose. But to make anything like a study of a celestial body, +the mounting must be an equatorial one; that is, one of the axes +around which the telescope moves must be inclined so as to point +towards the pole of the heavens, which is near the polar star. +This axis will then make an angle with the horizon equal to the +latitude of the place. The telescope cannot, however, be mounted +directly on this axis, but must be attached to a second one, +itself fastened to this one. + +[Illustration with caption: SECTION OF THE PRIMITIVE MOUNTING. P +P. Polar axis, bearing a fork at the upper end A. Declination axis +passing through the fork E. Section of telescope tube C. Weight to +balance the tube.] + +When mounted in this way, an object can be followed in its diurnal +motion from east to west by turning on the polar axis alone. But +if the greatest facility in use is required, this motion must be +performed by clock-work. A telescope with this appendage will +commonly cost one thousand dollars and upward, so that it is not +usually applied to very small ones. + +We will now suppose that the reader wishes to purchase a telescope +or an object-glass for himself, and to be able to judge of its +performance. He must have the object-glass properly adjusted in +its tube, and must use the highest power; that is, the smallest +eye-piece, which he intends to use in the instrument. Of course he +understands that in looking directly at a star or a celestial +object it must appear sharp in outline and well defined. But +without long practice with good instruments, this will not give +him a very definite idea. If the person who selects the telescope +is quite unpractised, it is possible that he can make the best +test by ascertaining at what distance he can read ordinary print. +To do this he should have an eye-piece magnifying about fifty +times for each inch of aperture of the telescope. For instance, if +his telescope is three inches clear aperture, then his eye-piece +should magnify one hundred and fifty times; if the aperture is +four inches, one magnifying two hundred times may be used. This +magnifying power is, as a general rule, about the highest that can +be advantageously used with any telescope. Supposing this +magnifying power to be used, this page should be legible at a +distance of four feet for every unit of magnifying power of the +telescope. For example, with a power of 100, it should be legible +at a distance of 400 feet; with a power of 200, at 800 feet, and +so on. To put the condition into another shape: if the telescope +will read the print at a distance of 150 feet for each inch of +aperture with the best magnifying power, its performance is at +least not very bad. If the magnifying power is less than would be +given by this rule, the telescope should perform a little better; +for instance, a three-inch telescope with a power of 60 should +make this page legible at a distance of 300 feet, or four feet for +each unit of power. + +The test applied by the optician is much more exact, and also more +easy. He points the instrument at a star, or at the reflection of +the sun's rays from a small round piece of glass or a globule of +quicksilver several hundred yards away, and ascertains whether the +rays are all brought to a focus. This is not done by simply +looking at the star, but by alternately pushing the eye-piece in +beyond the point of distinct vision and drawing it out past the +point. In this way the image of the star will appear, not as a +point, but as a round disk of light. If the telescope is perfect, +this disk will appear round and of uniform brightness in either +position of the eye-piece. But if there is any spherical +aberration or differences of density in different parts of the +glass, the image will appear distorted in various ways. If the +spherical aberration is not correct, the outer rim of the disk +will be brighter than the centre when the eye-piece is pushed in, +and the centre will be the brighter when it is drawn out. If the +curves of the glass are not even all around, the image will appear +oval in one or the other position. If there are large veins of +unequal density, wings or notches will be seen on the image. If +the atmosphere is steady, the image, when the eye-piece is pushed +in, will be formed of a great number of minute rings of light. If +the glass is good, these rings will be round, unbroken, and +equally bright. We present several figures showing how these +spectral images, as they are sometimes called, will appear; first, +when the eye-piece is pushed in, and secondly, when it is drawn +out, with telescopes of different qualities. + +We have thus far spoken only of the refracting telescope, because +it is the kind with which an observer would naturally seek to +supply himself. At the same time there is little doubt that the +construction of a reflector of moderate size is easier than that +of a corresponding refractor. The essential part of the reflector +is a slightly concave mirror of any metal which will bear a high +polish. This mirror may be ground and polished in the same way as +a lens, only the tool must be convex. + +[Illustration with caption: SPECTRAL IMAGES OF STARS; THE UPPER +LINE SHOWING HOW THEY APPEAR WITH THE EYE-PIECE PUSHED IN, THE +LOWER WITH THE EYE-PIECE DRAWN OUT. + +A The telescope is all right +B Spherical aberration shown by the light and dark centre +C The objective is not spherical but elliptical +D The glass not uniform--a very bad and incurable case +E One side of the objective nearer than the other. Adjust it] + +Of late years it has become very common to make the mirror of +glass and to cover the reflecting face with an exceedingly thin +film of silver, which can be polished by hand in a few minutes. +Such a mirror differs from our ordinary looking-glass in that the +coating of silver is put on the front surface, so that the light +does not pass through the glass. Moreover, the coating of silver +is so thin as to be almost transparent: in fact, the sun may be +seen through it by direct vision as a faint blue object. Silvered +glass reflectors made in this way are extensively manufactured in +London, and are far cheaper than refracting telescopes of +corresponding size. Their great drawback is the want of permanence +in the silver film. In the city the film will ordinarily tarnish +in a few months from the sulphurous vapors arising from gaslights +and other sources, and even in the country it is very difficult to +preserve the mirror from the contact of everything that will +injure it. In consequence, the possessor of such a telescope, if +he wishes to keep it in order, must always be prepared to resilver +and repolish it. To do this requires such careful manipulation and +management of the chemicals that it is hardly to be expected that +an amateur will take the trouble to keep his telescope in order, +unless he has a taste for chemistry as well as for astronomy. + +The curiosity to see the heavenly bodies through great telescopes +is so wide-spread that we are apt to forget how much can be seen +and done with small ones. The fact is that a large proportion of +the astronomical observations of past times have been made with +what we should now regard as very small instruments, and a good +deal of the solid astronomical work of the present time is done +with meridian circles the apertures of which ordinarily range from +four to eight inches. One of the most conspicuous examples in +recent times of how a moderate-sized instrument may be utilized is +afforded by the discoveries of double stars made by Mr. S. W. +Burnham, of Chicago. Provided with a little six-inch telescope, +procured at his own expense from the Messrs. Clark, he has +discovered many hundred double stars so difficult that they had +escaped the scrutiny of Maedler and the Struves, and gained for +himself one of the highest positions among the astronomers of the +day engaged in the observation of these objects. It was with this +little instrument that on Mount Hamilton, California--afterward +the site of the great Lick Observatory--he discovered forty-eight +new double stars, which had remained unnoticed by all previous +observers. First among the objects which show beautifully through +moderate instruments stands the moon. People who want to see the +moon at an observatory generally make the mistake of looking when +the moon is full, and asking to see it through the largest +telescope. Nothing can then be made out but a brilliant blaze of +light, mottled with dark spots, and crossed by irregular bright +lines. The best time to view the moon is near or before the first +quarter, or when she is from three to eight days old. The last +quarter is of course equally favorable, so far as seeing is +concerned, only one must be up after midnight to see her in that +position. Seen through a three or four inch telescope, a day or +two before the first quarter, about half an hour after sunset, and +with a magnifying power between fifty and one hundred, the moon is +one of the most beautiful objects in the heavens. Twilight softens +her radiance so that the eye is not dazzled as it will be when the +sky is entirely dark. The general aspect she then presents is that +of a hemisphere of beautiful chased silver carved out in curious +round patterns with a more than human skill. If, however, one +wishes to see the minute details of the lunar surface, in which +many of our astronomers are now so deeply interested, he must use +a higher magnifying power. The general beautiful effect is then +lessened, but more details are seen. Still, it is hardly necessary +to seek for a very large telescope for any investigation of the +lunar surface. I very much doubt whether any one has ever seen +anything on the moon which could not be made out in a clear, +steady atmosphere with a six-inch telescope of the first class. + +Next to the moon, Saturn is among the most beautiful of celestial +objects. Its aspect, however, varies with its position in its +orbit. Twice in the course of a revolution, which occupies nearly +thirty years, the rings are seen edgewise, and for a few days are +invisible even in a powerful telescope. For an entire year their +form may be difficult to make out with a small telescope. These +unfavorable conditions occur in 1907 and 1921. Between these +dates, especially for some years after 1910, the position of the +planet in the sky will be the most favorable, being in northern +declination, near its perihelion, and having its rings widely +open. We all know that Saturn is plainly visible to the naked eye, +shining almost like a star of the first magnitude, so that there +is no difficulty in finding it if one knows when and where to +look. In 1906-1908 its oppositions occur in the month of +September. In subsequent years, it will occur a month later every +two and a half years. The ring can be seen with a common, good +spy-glass fastened to a post so as to be steady. A four or five- +inch telescope will show most of the satellites, the division in +the ring, and, when the ring is well opened, the curious dusky +ring discovered by Bond. This "crape ring," as it is commonly +called, is one of the most singular phenomena presented by that +planet. + +It might be interesting to the amateur astronomer with a keen eye +and a telescope of four inches aperture or upward to frequently +scrutinize Saturn, with a view of detecting any extraordinary +eruptions upon his surface, like that seen by Professor Hall in +1876. On December 7th of that year a bright spot was seen upon +Saturn's equator. It elongated itself from day to day, and +remained visible for several weeks. Such a thing had never before +been known upon this planet, and had it not been that Professor +Hall was engaged in observations upon the satellites, it would not +have been seen then. A similar spot on the planet was recorded in +1902, and much more extensively noticed. On this occasion the spot +appeared in a higher latitude from the planet's equator than did +Professor Hall's. At this appearance the time of the planet's +revolution on its axis was found to be somewhat greater than in +1876, in accordance with the general law exhibited in the +rotations of the sun and of Jupiter. Notwithstanding their +transient character, these two spots have afforded the only +determination of the time of revolution of Saturn which has been +made since Herschel the elder. + +[Illustration with caption: THE GREAT REFRACTOR OF THE NATIONAL +OBSERVATORY AT WASHINGTON] + +Of the satellites of Saturn the brightest is Titan, which can be +seen with the smallest telescope, and revolves around the planet +in fifteen days. Iapetus, the outer satellite, is remarkable for +varying greatly in brilliancy during its revolution around the +planet. Any one having the means and ability to make accurate +photometrical estimates of the light of this satellite in all +points of its orbit, can thereby render a valuable service to +astronomy. + +The observations of Venus, by which the astronomers of the last +century supposed themselves to have discovered its time of +rotation on its axis, were made with telescopes much inferior to +ours. Although their observations have not been confirmed, some +astronomers are still inclined to think that their results have +not been refuted by the failure of recent observers to detect +those changes which the older ones describe on the surface of the +planet. With a six-inch telescope of the best quality, and with +time to choose the most favorable moment, one will be as well +equipped to settle the question of the rotation of Venus as the +best observer. The few days near each inferior conjunction are +especially to be taken advantage of. + +The questions to be settled are two: first, are there any dark +spots or other markings on the disk? second, are there any +irregularities in the form of the sharp cusps? The central +portions of the disk are much darker than the outline, and it is +probably this fact which has given rise to the impression of dark +spots. Unless this apparent darkness changes from time to time, or +shows some irregularity in its outline, it cannot indicate any +rotation of the planet. The best time to scrutinize the sharp +cusps will be when the planet is nearly on the line from the earth +to the sun. The best hour of the day is near sunset, the half-hour +following sunset being the best of all. But if Venus is near the +sun, she will after sunset be too low down to be well seen, and +must be looked at late in the afternoon. + +The planet Mars must always be an object of great interest, +because of all the heavenly bodies it is that which appears to +bear the greatest resemblance to the earth. It comes into +opposition at intervals of a little more than two years, and can +be well seen only for a month or two before and after each +opposition. It is hopeless to look for the satellites of Mars with +any but the greatest telescopes of the world. But the markings on +the surface, from which the time of rotation has been determined, +and which indicate a resemblance to the surface of our own planet, +can be well seen with telescopes of six inches aperture and +upward. One or both of the bright polar spots, which are supposed +to be due to deposits of snow, can be seen with smaller telescopes +when the situation of the planet is favorable. + +The case is different with the so-called canals discovered by +Schiaparelli in 1877, which have ever since excited so much +interest, and given rise to so much discussion as to their nature. +The astronomer who has had the best opportunities for studying +them is Mr. Percival Lowell, whose observatory at Flaggstaff, +Arizona, is finely situated for the purpose, while he also has one +of the best if not the largest of telescopes. There the canals are +seen as fine dark lines; but, even then, they must be fifty miles +in breadth, so that the word "canal" may be regarded as a +misnomer. + +Although the planet Jupiter does not present such striking +features as Saturn, it is of even more interest to the amateur +astronomer, because he can study it with less optical power, and +see more of the changes upon its surface. Every work on astronomy +tells in a general way of the belts of Jupiter, and many speculate +upon their causes. The reader of recent works knows that Jupiter +is supposed to be not a solid mass like the earth, but a great +globe of molten and vaporous matter, intermediate in constitution +between the earth and the sun. The outer surface which we see is +probably a hot mass of vapor hundreds of miles deep, thrown up +from the heated interior. The belts are probably cloudlike forms +in this vaporous mass. Certain it is that they are continually +changing, so that the planet seldom looks exactly the same on two +successive evenings. The rotation of the planet can be very well +seen by an hour's watching. In two hours an object at the centre +of the disk will move off to near the margin. + +The satellites of this planet, in their ever-varying phases, are +objects of perennial interest. Their eclipses may be observed with +a very small telescope, if one knows when to look for them. To do +this successfully, and without waste of time, it is necessary to +have an astronomical ephemeris for the year. All the observable +phenomena are there predicted for the convenience of observers. +Perhaps the most curious observation to be made is that of the +shadow of the satellite crossing the disk of Jupiter. The writer +has seen this perfectly with a six-inch telescope, and a much +smaller one would probably show it well. With a telescope of this +size, or a little larger, the satellites can be seen between us +and Jupiter. Sometimes they appear a little brighter than the +planet, and sometimes a little fainter. + +Of the remaining large planets, Mercury, the inner one, and Uranus +and Neptune, the two outer ones, are of less interest than the +others to an amateur with a small telescope, because they are more +difficult to see. Mercury can, indeed, be observed with the +smallest instrument, but no physical configurations or changes +have ever been made out upon his surface. The question whether any +such can be observed is still an open one, which can be settled +only by long and careful scrutiny. A small telescope is almost as +good for this purpose as a large one, because the atmospheric +difficulties in the way of getting a good view of the planet +cannot be lessened by an increase of telescopic power. + +Uranus and Neptune are so distant that telescopes of considerable +size and high magnifying power are necessary to show their disks. +In small telescopes they have the appearance of stars, and the +observer has no way of distinguishing them from the surrounding +stars unless he can command the best astronomical appliances, such +as star maps, circles on his instrument, etc. It is, however, to +be remarked, as a fact not generally known, that Uranus can be +well seen with the naked eye if one knows where to look for it. To +recognize it, it is necessary to have an astronomical ephemeris +showing its right ascension and declination, and star maps showing +where the parallels of right ascension and declination lie among +the stars. When once found by the naked eye, there will, of +course, be no difficulty in pointing the telescope upon it. + +Of celestial objects which it is well to keep a watch upon, and +which can be seen to good advantage with inexpensive instruments, +the sun may be considered as holding the first place. Astronomers +who make a specialty of solar physics have, especially in this +country, so many other duties, and their view is so often +interrupted by clouds, that a continuous record of the spots on +the sun and the changes they undergo is hardly possible. Perhaps +one of the most interesting and useful pieces of astronomical work +which an amateur can perform will consist of a record of the +origin and changes of form of the solar spots and faculae. What +does a spot look like when it first comes into sight? Does it +immediately burst forth with considerable magnitude, or does it +begin as the smallest visible speck, and gradually grow? When +several spots coalesce into one, how do they do it? When a spot +breaks up into several pieces, what is the seeming nature of the +process? How do the groups of brilliant points called faculae +come, change, and grow? All these questions must no doubt be +answered in various ways, according to the behavior of the +particular spot, but the record is rather meagre, and the +conscientious and industrious amateur will be able to amuse +himself by adding to it, and possibly may make valuable +contributions to science in the same way. + +Still another branch of astronomical observation, in which +industry and skill count for more than expensive instruments, is +the search for new comets. This requires a very practised eye, in +order that the comet may be caught among the crowd of stars which +flit across the field of view as the telescope is moved. It is +also necessary to be well acquainted with a number of nebulae +which look very much like comets. The search can be made with +almost any small telescope, if one is careful to use a very low +power. With a four-inch telescope a power not exceeding twenty +should be employed. To search with ease, and in the best manner, +the observer should have what among astronomers is familiarly +known as a "broken-backed telescope." This instrument has the eye- +piece on the end of the axis, where one would never think of +looking for it. By turning the instrument on this axis, it sweeps +from one horizon through the zenith and over to the other horizon +without the observer having to move his head. This is effected by +having a reflector in the central part of the instrument, which +throws the rays of light at right angles through the axis. + +[Illustration: THE "BROKEN-BACKED COMET-SEEKER"] + +How well this search can be conducted by observers with limited +means at their disposal is shown by the success of several +American observers, among whom Messrs. W. R. Brooks, E. E. +Barnard, and Lewis Swift are well known. The cometary discoveries +of these men afford an excellent illustration of how much can be +done with the smallest means when one sets to work in the right +spirit. + +The larger number of wonderful telescopic objects are to be sought +for far beyond the confines of the solar system, in regions from +which light requires years to reach us. On account of their great +distance, these objects generally require the most powerful +telescopes to be seen in the best manner; but there are quite a +number within the range of the amateur. Looking at the Milky Way, +especially its southern part, on a clear winter or summer evening, +tufts of light will be seen here and there. On examining these +tufts with a telescope, they will be found to consist of congeries +of stars. Many of these groups are of the greatest beauty, with +only a moderate optical power. Of all the groups in the Milky Way +the best known is that in the sword-handle of Perseus, which may +be seen during the greater part of the year, and is distinctly +visible to the naked eye as a patch of diffused light. With the +telescope there are seen in this patch two closely connected +clusters of stars, or perhaps we ought rather to say two centres +of condensation. + +Another object of the same class is Proesepe in the constellation +Cancer. This can be very distinctly seen by the naked eye on a +clear moonless night in winter or spring as a faint nebulous +object, surrounded by three small stars. The smallest telescope +shows it as a group of stars. + +Of all stellar objects, the great nebula of Orion is that which +has most fascinated the astronomers of two centuries. It is +distinctly visible to the naked eye, and may be found without +difficulty on any winter night. The three bright stars forming the +sword-belt of Orion are known to every one who has noticed that +constellation. Below this belt is seen another triplet of stars, +not so bright, and lying in a north and south direction. The +middle star of this triplet is the great nebula. At first the +naked eye sees nothing to distinguish it from other stars, but if +closely scanned it will be seen to have a hazy aspect. A four-inch +telescope will show its curious form. Not the least interesting of +its features are the four stars known as the "Trapezium," which +are located in a dark region near its centre. In fact, the whole +nebula is dotted with stars, which add greatly to the effect +produced by its mysterious aspect. + +The great nebula of Andromeda is second only to that of Orion in +interest. Like the former, it is distinctly visible to the naked +eye, having the aspect of a faint comet. The most curious feature +of this object is that although the most powerful telescopes do +not resolve it into stars, it appears in the spectroscope as if it +were solid matter shining by its own light. + +The above are merely selections from the countless number of +objects which the heavens offer to telescopic study. Many such are +described in astronomical works, but the amateur can gratify his +curiosity to almost any extent by searching them out for himself. + +[Illustration with caption: NEBULA IN ORION] + +Ever since 1878 a red spot, unlike any before noticed, has +generally been visible on Jupiter. At first it was for several +years a very conspicuous object, but gradually faded away, so that +since 1890 it has been made out only with difficulty. But it is +now regarded as a permanent feature of the planet. There is some +reason to believe it was occasionally seen long before attention +was first attracted to it. Doubtless, when it can be seen at all, +practice in observing such objects is more important than size of +telescope. + + + + + +VI + +WHAT THE ASTRONOMERS ARE DOING + + +In no field of science has human knowledge been more extended in +our time than in that of astronomy. Forty years ago astronomical +research seemed quite barren of results of great interest or value +to our race. The observers of the world were working on a +traditional system, grinding out results in an endless course, +without seeing any prospect of the great generalizations to which +they might ultimately lead. Now this is all changed. A new +instrument, the spectroscope, has been developed, the extent of +whose revelations we are just beginning to learn, although it has +been more than thirty years in use. The application of photography +has been so extended that, in some important branches of +astronomical work, the observer simply photographs the phenomenon +which he is to study, and then makes his observation on the +developed negative. + +The world of astronomy is one of the busiest that can be found to- +day, and the writer proposes, with the reader's courteous consent, +to take him on a stroll through it and see what is going on. We +may begin our inspection with a body which is, for us, next to the +earth, the most important in the universe. I mean the sun. At the +Greenwich Observatory the sun has for more than twenty years been +regularly photographed on every clear day, with the view of +determining the changes going on in its spots. In recent years +these observations have been supplemented by others, made at +stations in India and Mauritius, so that by the combination of all +it is quite exceptional to have an entire day pass without at +least one photograph being taken. On these observations must +mainly rest our knowledge of the curious cycle of change in the +solar spots, which goes through a period of about eleven years, +but of which no one has as yet been able to establish the cause. + +This Greenwich system has been extended and improved by an +American. Professor George E. Hale, formerly Director of the +Yerkes Observatory, has devised an instrument for taking +photographs of the sun by a single ray of the spectrum. The light +emitted by calcium, the base of lime, and one of the substances +most abundant in the sun, is often selected to impress the plate. + +The Carnegie Institution has recently organized an enterprise for +carrying on the study of the sun under a combination of better +conditions than were ever before enjoyed. The first requirement in +such a case is the ablest and most enthusiastic worker in the +field, ready to devote all his energies to its cultivation. This +requirement is found in the person of Professor Hale himself. The +next requirement is an atmosphere of the greatest transparency, +and a situation at a high elevation above sea-level, so that the +passage of light from the sun to the observer shall be obstructed +as little as possible by the mists and vapors near the earth's +surface. This requirement is reached by placing the observatory on +Mount Wilson, near Pasadena, California, where the climate is +found to be the best of any in the United States, and probably not +exceeded by that of any other attainable point in the world. The +third requirement is the best of instruments, specially devised to +meet the requirements. In this respect we may be sure that nothing +attainable by human ingenuity will be found wanting. + +Thus provided, Professor Hale has entered upon the task of +studying the sun, and recording from day to day all the changes +going on in it, using specially devised instruments for each +purpose in view. Photography is made use of through almost the +entire investigation. A full description of the work would require +an enumeration of technical details, into which we need not enter +at present. Let it, therefore, suffice to say in a general way +that the study of the sun is being carried on on a scale, and with +an energy worthy of the most important subject that presents +itself to the astronomer. Closely associated with this work is +that of Professor Langley and Dr. Abbot, at the Astro-Physical +Observatory of the Smithsonian Institution, who have recently +completed one of the most important works ever carried out on the +light of the sun. They have for years been analyzing those of its +rays which, although entirely invisible to our eyes, are of the +same nature as those of light, and are felt by us as heat. To do +this, Langley invented a sort of artificial eye, which he called a +bolometer, in which the optic nerve is made of an extremely thin +strip of metal, so slight that one can hardly see it, which is +traversed by an electric current. This eye would be so dazzled by +the heat radiated from one's body that, when in use, it must be +protected from all such heat by being enclosed in a case kept at a +constant temperature by being immersed in water. With this eye the +two observers have mapped the heat rays of the sun down to an +extent and with a precision which were before entirely unknown. + +The question of possible changes in the sun's radiation, and of +the relation of those changes to human welfare, still eludes our +scrutiny. With all the efforts that have been made, the physicist +of to-day has not yet been able to make anything like an exact +determination of the total amount of heat received from the sun. +The largest measurements are almost double the smallest. This is +partly due to the atmosphere absorbing an unknown and variable +fraction of the sun's rays which pass through it, and partly to +the difficulty of distinguishing the heat radiated by the sun from +that radiated by terrestrial objects. + +In one recent instance, a change in the sun's radiation has been +noticed in various parts of the world, and is of especial interest +because there seems to be little doubt as to its origin. In the +latter part of 1902 an extraordinary diminution was found in the +intensity of the sun's heat, as measured by the bolometer and +other instruments. This continued through the first part of 1903, +with wide variations at different places, and it was more than a +year after the first diminution before the sun's rays again +assumed their ordinary intensity. + +This result is now attributed to the eruption of Mount Pelee, +during which an enormous mass of volcanic dust and vapor was +projected into the higher regions of the air, and gradually +carried over the entire earth by winds and currents. Many of our +readers may remember that something yet more striking occurred +after the great cataclasm at Krakatoa in 1883, when, for more than +a year, red sunsets and red twilights of a depth of shade never +before observed were seen in every part of the world. + +What we call universology--the knowledge of the structure and +extent of the universe--must begin with a study of the starry +heavens as we see them. There are perhaps one hundred million +stars in the sky within the reach of telescopic vision. This +number is too great to allow of all the stars being studied +individually; yet, to form the basis for any conclusion, we must +know the positions and arrangement of as many of them as we can +determine. + +To do this the first want is a catalogue giving very precise +positions of as many of the brighter stars as possible. The +principal national observatories, as well as some others, are +engaged in supplying this want. Up to the present time about +200,000 stars visible in our latitudes have been catalogued on +this precise plan, and the work is still going on. In that part of +the sky which we never see, because it is only visible from the +southern hemisphere, the corresponding work is far from being as +extensive. Sir David Gill, astronomer at the Cape of Good Hope, +and also the directors of other southern observatories, are +engaged in pushing it forward as rapidly as the limited facilities +at their disposal will allow. + +Next in order comes the work of simply listing as many stars as +possible. Here the most exact positions are not required. It is +only necessary to lay down the position of each star with +sufficient exactness to distinguish it from all its neighbors. +About 400,000 stars were during the last half-century listed in +this way at the observatory of Bonn by Argelander, Schonfeld, and +their assistants. This work is now being carried through the +southern hemisphere on a large scale by Thome, Director of the +Cordoba Observatory, in the Argentine Republic. This was founded +thirty years ago by our Dr. B. A. Gould, who turned it over to Dr. +Thome in 1886. The latter has, up to the present time, fixed and +published the positions of nearly half a million stars. This work +of Thome extends to fainter stars than any other yet attempted, so +that, as it goes on, we have more stars listed in a region +invisible in middle northern latitudes than we have for that part +of the sky we can see. Up to the present time three quarto volumes +giving the positions and magnitudes of the stars have appeared. +Two or three volumes more, and, perhaps, ten or fifteen years, +will be required to complete the work. + +About twenty years ago it was discovered that, by means of a +telescope especially adapted to this purpose, it was possible to +photograph many more stars than an instrument of the same size +would show to the eye. This discovery was soon applied in various +quarters. Sir David Gill, with characteristic energy, photographed +the stars of the southern sky to the number of nearly half a +million. As it was beyond his power to measure off and compute the +positions of the stars from his plates, the latter were sent to +Professor J. C. Kapteyn, of Holland, who undertook the enormous +labor of collecting them into a catalogue, the last volume of +which was published in 1899. One curious result of this enterprise +is that the work of listing the stars is more complete for the +southern hemisphere than for the northern. + +Another great photographic work now in progress has to do with the +millions of stars which it is impossible to handle individually. +Fifteen years ago an association of observatories in both +hemispheres undertook to make a photographic chart of the sky on +the largest scale. Some portions of this work are now approaching +completion, but in others it is still in a backward state, owing +to the failure of several South American observatories to carry +out their part of the programme. When it is all done we shall have +a picture of the sky, the study of which may require the labor of +a whole generation of astronomers. + +Quite independently of this work, the Harvard University, under +the direction of Professor Pickering, keeps up the work of +photographing the sky on a surprising scale. On this plan we do +not have to leave it to posterity to learn whether there is any +change in the heavens, for one result of the enterprise has been +the discovery of thirteen of the new stars which now and then +blaze out in the heavens at points where none were before known. +Professor Pickering's work has been continually enlarged and +improved until about 150,000 photographic plates, showing from +time to time the places of countless millions of stars among their +fellows are now stored at the Harvard Observatory. Not less +remarkable than this wealth of material has been the development +of skill in working it up. Some idea of the work will be obtained +by reflecting that, thirty years ago, careful study of the heavens +by astronomers devoting their lives to the task had resulted in +the discovery of some two or three hundred stars, varying in their +light. Now, at Harvard, through keen eyes studying and comparing +successive photographs not only of isolated stars, but of clusters +and agglomerations of stars in the Milky Way and elsewhere, +discoveries of such objects numbering hundreds have been made, and +the work is going on with ever-increasing speed. Indeed, the +number of variable stars now known is such that their study as +individual objects no longer suffices, and they must hereafter be +treated statistically with reference to their distribution in +space, and their relations to one another, as a census classifies +the entire population without taking any account of individuals. + +The works just mentioned are concerned with the stars. But the +heavenly spaces contain nebulae as well as stars; and photography +can now be even more successful in picturing them than the stars. +A few years ago the late lamented Keeler, at the Lick Observatory, +undertook to see what could be done by pointing the Crossley +reflecting telescope at the sky and putting a sensitive +photographic plate in the focus. He was surprised to find that a +great number of nebulae, the existence of which had never before +been suspected, were impressed on the plate. Up to the present +time the positions of about 8000 of these objects have been +listed. Keeler found that there were probably 200,000 nebulae in +the heavens capable of being photographed with the Crossley +reflector. But the work of taking these photographs is so great, +and the number of reflecting telescopes which can be applied to it +so small, that no one has ventured to seriously commence it. It is +worthy of remark that only a very small fraction of these objects +which can be photographed are visible to the eye, even with the +most powerful telescope. + +This demonstration of what the reflecting telescope can do may be +regarded as one of the most important discoveries of our time as +to the capabilities of astronomical instruments. It has long been +known that the image formed in the focus of the best refracting +telescope is affected by an imperfection arising from the +different action of the glasses on rays of light of different +colors. Hence, the image of a star can never be seen or +photographed with such an instrument, as an actual point, but only +as a small, diffused mass. This difficulty is avoided in the +reflecting telescope; but a new difficulty is found in the bending +of the mirror under the influence of its own weight. Devices for +overcoming this had been so far from successful that, when Mr. +Crossley presented his instrument to the Lick Observatory, it was +feared that little of importance could be done with it. But as +often happens in human affairs outside the field of astronomy, +when ingenious and able men devote their attention to the careful +study of a problem, it was found that new results could be +reached. Thus it was that, before a great while, what was supposed +to be an inferior instrument proved not only to have qualities not +before suspected, but to be the means of making an important +addition to the methods of astronomical investigation. + +In order that our knowledge of the position of a star may be +complete, we must know its distance. This can be measured only +through the star's parallax--that is to say, the slight change in +its direction produced by the swing of our earth around its orbit. +But so vast is the distance in question that this change is +immeasurably small, except for, perhaps, a few hundred stars, and +even for these few its measurement almost baffles the skill of the +most expert astronomer. Progress in this direction is therefore +very slow, and there are probably not yet a hundred stars of which +the parallax has been ascertained with any approach to certainty. +Dr. Chase is now completing an important work of this kind at the +Yale Observatory. + +To the most refined telescopic observations, as well as to the +naked eye, the stars seem all alike, except that they differ +greatly in brightness, and somewhat in color. But when their light +is analyzed by the spectroscope, it is found that scarcely any two +are exactly alike. An important part of the work of the astro- +physical observatories, especially that of Harvard, consists in +photographing the spectra of thousands of stars, and studying the +peculiarities thus brought out. At Harvard a large portion of this +work is done as part of the work of the Henry Draper Memorial, +established by his widow in memory of the eminent investigator of +New York, who died twenty years ago. + +By a comparison of the spectra of stars Sir William Huggins has +developed the idea that these bodies, like human beings, have a +life history. They are nebulae in infancy, while the progress to +old age is marked by a constant increase in the density of their +substance. Their temperature also changes in a way analogous to +the vigor of the human being. During a certain time the star +continually grows hotter and hotter. But an end to this must come, +and it cools off in old age. What the age of a star may be is hard +even to guess. It is many millions of years, perhaps hundreds, +possibly even thousands, of millions. + +Some attempt at giving the magnitude is included in every +considerable list of stars. The work of determining the magnitudes +with the greatest precision is so laborious that it must go on +rather slowly. It is being pursued on a large scale at the Harvard +Observatory, as well as in that of Potsdam, Germany. + +We come now to the question of changes in the appearance of bright +stars. It seems pretty certain that more than one per cent of +these bodies fluctuate to a greater or less extent in their light. +Observations of these fluctuations, in the case of at least the +brighter stars, may be carried on without any instrument more +expensive than a good opera-glass--in fact, in the case of stars +visible to the naked eye, with no instrument at all. + +As a general rule, the light of these stars goes through its +changes in a regular period, which is sometimes as short as a few +hours, but generally several days, frequently a large fraction of +a year or even eighteen months. Observations of these stars are +made to determine the length of the period and the law of +variation of the brightness. Any person with a good eye and skill +in making estimates can make the observations if he will devote +sufficient pains to training himself; but they require a degree of +care and assiduity which is not to be expected of any one but an +enthusiast on the subject. One of the most successful observers of +the present time is Mr. W. A. Roberts, a resident of South Africa, +whom the Boer war did not prevent from keeping up a watch of the +southern sky, which has resulted in greatly increasing our +knowledge of variable stars. There are also quite a number of +astronomers in Europe and America who make this particular study +their specialty. + +During the past fifteen years the art of measuring the speed with +which a star is approaching us or receding from us has been +brought to a wonderful degree of perfection. The instrument with +which this was first done was the spectroscope; it is now replaced +with another of the same general kind, called the spectrograph. +The latter differs from the other only in that the spectrum of the +star is photographed, and the observer makes his measures on the +negative. This method was first extensively applied at the Potsdam +Observatory in Germany, and has lately become one of the +specialties of the Lick Observatory, where Professor Campbell has +brought it to its present degree of perfection. The Yerkes +Observatory is also beginning work in the same line, where +Professor Frost is already rivalling the Lick Observatory in the +precision of his measures. + +Let us now go back to our own little colony and see what is being +done to advance our knowledge of the solar system. This consists +of planets, on one of which we dwell, moons revolving around them, +comets, and meteoric bodies. The principal national observatories +keep up a more or less orderly system of observations of the +positions of the planets and their satellites in order to +determine the laws of their motion. As in the case of the stars, +it is necessary to continue these observations through long +periods of time in order that everything possible to learn may be +discovered. + +Our own moon is one of the enigmas of the mathematical astronomer. +Observations show that she is deviating from her predicted place, +and that this deviation continues to increase. True, it is not +very great when measured by an ordinary standard. The time at +which the moon's shadow passed a given point near Norfolk during +the total eclipse of May 29, 1900, was only about seven seconds +different from the time given in the Astronomical Ephemeris. The +path of the shadow along the earth was not out of place by more +than one or two miles But, small though these deviations are, they +show that something is wrong, and no one has as yet found out what +it is. Worse yet, the deviation is increasing rapidly. The +observers of the total eclipse in August, 1905, were surprised to +find that it began twenty seconds before the predicted time. The +mathematical problems involved in correcting this error are of +such complexity that it is only now and then that a mathematician +turns up anywhere in the world who is both able and bold enough to +attack them. + +There now seems little doubt that Jupiter is a miniature sun, only +not hot enough at its surface to shine by its own light The point +in which it most resembles the sun is that its equatorial regions +rotate in less time than do the regions near the poles. This shows +that what we see is not a solid body. But none of the careful +observers have yet succeeded in determining the law of this +difference of rotation. + +Twelve years ago a suspicion which had long been entertained that +the earth's axis of rotation varied a little from time to time was +verified by Chandler. The result of this is a slight change in the +latitude of all places on the earth's surface, which admits of +being determined by precise observations. The National Geodetic +Association has established four observatories on the same +parallel of latitude--one at Gaithersburg, Maryland, another on +the Pacific coast, a third in Japan, and a fourth in Italy--to +study these variations by continuous observations from night to +night. This work is now going forward on a well-devised plan. + +A fact which will appeal to our readers on this side of the +Atlantic is the success of American astronomers. Sixty years ago +it could not be said that there was a well-known observatory on +the American continent. The cultivation of astronomy was confined +to a professor here and there, who seldom had anything better than +a little telescope with which he showed the heavenly bodies to his +students. But during the past thirty years all this has been +changed. The total quantity of published research is still less +among us than on the continent of Europe, but the number of men +who have reached the highest success among us may be judged by one +fact. The Royal Astronomical Society of England awards an annual +medal to the English or foreign astronomer deemed most worthy of +it. The number of these medals awarded to Americans within twenty- +five years is about equal to the number awarded to the astronomers +of all other nations foreign to the English. That this +preponderance is not growing less is shown by the award of medals +to Americans in three consecutive years--1904, 1905, and 1906. +The recipients were Hale, Boss, and Campbell. Of the fifty foreign +associates chosen by this society for their eminence in +astronomical research, no less than eighteen--more than one-third +--are Americans. + + + + + +VII + +LIFE IN THE UNIVERSE + + +So far as we can judge from what we see on our globe, the +production of life is one of the greatest and most incessant +purposes of nature. Life is absent only in regions of perpetual +frost, where it never has an opportunity to begin; in places where +the temperature is near the boiling-point, which is found to be +destructive to it; and beneath the earth's surface, where none of +the changes essential to it can come about. Within the limits +imposed by these prohibitory conditions--that is to say, within +the range of temperature at which water retains its liquid state, +and in regions where the sun's rays can penetrate and where wind +can blow and water exist in a liquid form--life is the universal +rule. How prodigal nature seems to be in its production is too +trite a fact to be dwelt upon. We have all read of the millions of +germs which are destroyed for every one that comes to maturity. +Even the higher forms of life are found almost everywhere. Only +small islands have ever been discovered which were uninhabited, +and animals of a higher grade are as widely diffused as man. + +If it would be going too far to claim that all conditions may have +forms of life appropriate to them, it would be going as much too +far in the other direction to claim that life can exist only with +the precise surroundings which nurture it on this planet. It is +very remarkable in this connection that while in one direction we +see life coming to an end, in the other direction we see it +flourishing more and more up to the limit. These two directions +are those of heat and cold. We cannot suppose that life would +develop in any important degree in a region of perpetual frost, +such as the polar regions of our globe. But we do not find any end +to it as the climate becomes warmer. On the contrary, every one +knows that the tropics are the most fertile regions of the globe +in its production. The luxuriance of the vegetation and the number +of the animals continually increase the more tropical the climate +becomes. Where the limit may be set no one can say. But it would +doubtless be far above the present temperature of the equatorial +regions. + +It has often been said that this does not apply to the human race, +that men lack vigor in the tropics. But human vigor depends on so +many conditions, hereditary and otherwise, that we cannot regard +the inferior development of humanity in the tropics as due solely +to temperature. Physically considered, no men attain a better +development than many tribes who inhabit the warmer regions of the +globe. The inferiority of the inhabitants of these regions in +intellectual power is more likely the result of race heredity than +of temperature. + +We all know that this earth on which we dwell is only one of +countless millions of globes scattered through the wilds of +infinite space. So far as we know, most of these globes are wholly +unlike the earth, being at a temperature so high that, like our +sun, they shine by their own light. In such worlds we may regard +it as quite certain that no organized life could exist. But +evidence is continually increasing that dark and opaque worlds +like ours exist and revolve around their suns, as the earth on +which we dwell revolves around its central luminary. Although the +number of such globes yet discovered is not great, the +circumstances under which they are found lead us to believe that +the actual number may be as great as that of the visible stars +which stud the sky. If so, the probabilities are that millions of +them are essentially similar to our own globe. Have we any reason +to believe that life exists on these other worlds? + +The reader will not expect me to answer this question positively. +It must be admitted that, scientifically, we have no light upon +the question, and therefore no positive grounds for reaching a +conclusion. We can only reason by analogy and by what we know of +the origin and conditions of life around us, and assume that the +same agencies which are at play here would be found at play under +similar conditions in other parts of the universe. + +If we ask what the opinion of men has been, we know historically +that our race has, in all periods of its history, peopled other +regions with beings even higher in the scale of development than +we are ourselves. The gods and demons of an earlier age all +wielded powers greater than those granted to man--powers which +they could use to determine human destiny. But, up to the time +that Copernicus showed that the planets were other worlds, the +location of these imaginary beings was rather indefinite. It was +therefore quite natural that when the moon and planets were found +to be dark globes of a size comparable with that of the earth +itself, they were made the habitations of beings like unto +ourselves. + +The trend of modern discovery has been against carrying this view +to its extreme, as will be presently shown. Before considering the +difficulties in the way of accepting it to the widest extent, let +us enter upon some preliminary considerations as to the origin and +prevalence of life, so far as we have any sound basis to go upon. + +A generation ago the origin of life upon our planet was one of the +great mysteries of science. All the facts brought out by +investigation into the past history of our earth seemed to show, +with hardly the possibility of a doubt, that there was a time when +it was a fiery mass, no more capable of serving as the abode of a +living being than the interior of a Bessemer steel furnace. There +must therefore have been, within a certain period, a beginning of +life upon its surface. But, so far as investigation had gone-- +indeed, so far as it has gone to the present time--no life has +been found to originate of itself. The living germ seems to be +necessary to the beginning of any living form. Whence, then, came +the first germ? Many of our readers may remember a suggestion by +Sir William Thomson, now Lord Kelvin, made twenty or thirty years +ago, that life may have been brought to our planet by the falling +of a meteor from space. This does not, however, solve the +difficulty--indeed, it would only make it greater. It still +leaves open the question how life began on the meteor; and +granting this, why it was not destroyed by the heat generated as +the meteor passed through the air. The popular view that life +began through a special act of creative power seemed to be almost +forced upon man by the failure of science to discover any other +beginning for it. It cannot be said that even to-day anything +definite has been actually discovered to refute this view. All we +can say about it is that it does not run in with the general views +of modern science as to the beginning of things, and that those +who refuse to accept it must hold that, under certain conditions +which prevail, life begins by a very gradual process, similar to +that by which forms suggesting growth seem to originate even under +conditions so unfavorable as those existing in a bottle of acid. + +But it is not at all necessary for our purpose to decide this +question. If life existed through a creative act, it is absurd to +suppose that that act was confined to one of the countless +millions of worlds scattered through space. If it began at a +certain stage of evolution by a natural process, the question will +arise, what conditions are favorable to the commencement of this +process? Here we are quite justified in reasoning from what, +granting this process, has taken place upon our globe during its +past history. One of the most elementary principles accepted by +the human mind is that like causes produce like effects. The +special conditions under which we find life to develop around us +may be comprehensively summed up as the existence of water in the +liquid form, and the presence of nitrogen, free perhaps in the +first place, but accompanied by substances with which it may form +combinations. Oxygen, hydrogen, and nitrogen are, then, the +fundamental requirements. The addition of calcium or other forms +of matter necessary to the existence of a solid world goes without +saying. The question now is whether these necessary conditions +exist in other parts of the universe. + +The spectroscope shows that, so far as the chemical elements go, +other worlds are composed of the same elements as ours. Hydrogen +especially exists everywhere, and we have reason to believe that +the same is true of oxygen and nitrogen. Calcium, the base of +lime, is almost universal. So far as chemical elements go, we may +therefore take it for granted that the conditions under which life +begins are very widely diffused in the universe. It is, therefore, +contrary to all the analogies of nature to suppose that life began +only on a single world. + +It is a scientific inference, based on facts so numerous as not to +admit of serious question, that during the history of our globe +there has been a continually improving development of life. As +ages upon ages pass, new forms are generated, higher in the scale +than those which preceded them, until at length reason appears and +asserts its sway. In a recent well-known work Alfred Russel +Wallace has argued that this development of life required the +presence of such a rare combination of conditions that there is no +reason to suppose that it prevailed anywhere except on our earth. +It is quite impossible in the present discussion to follow his +reasoning in detail; but it seems to me altogether inconclusive. +Not only does life, but intelligence, flourish on this globe under +a great variety of conditions as regards temperature and +surroundings, and no sound reason can be shown why under certain +conditions, which are frequent in the universe, intelligent beings +should not acquire the highest development. + +Now let us look at the subject from the view of the mathematical +theory of probabilities. A fundamental tenet of this theory is +that no matter how improbable a result may be on a single trial, +supposing it at all possible, it is sure to occur after a +sufficient number of trials--and over and over again if the trials +are repeated often enough. For example, if a million grains of +corn, of which a single one was red, were all placed in a pile, +and a blindfolded person were required to grope in the pile, +select a grain, and then put it back again, the chances would be a +million to one against his drawing out the red grain. If drawing +it meant he should die, a sensible person would give himself no +concern at having to draw the grain. The probability of his death +would not be so great as the actual probability that he will +really die within the next twenty-four hours. And yet if the whole +human race were required to run this chance, it is certain that +about fifteen hundred, or one out of a million, of the whole human +family would draw the red grain and meet his death. + +Now apply this principle to the universe. Let us suppose, to fix +the ideas, that there are a hundred million worlds, but that the +chances are one thousand to one against any one of these taken at +random being fitted for the highest development of life or for the +evolution of reason. The chances would still be that one hundred +thousand of them would be inhabited by rational beings whom we +call human. But where are we to look for these worlds? This no man +can tell. We only infer from the statistics of the stars--and this +inference is fairly well grounded--that the number of worlds +which, so far as we know, may be inhabited, are to be counted by +thousands, and perhaps by millions. + +In a number of bodies so vast we should expect every variety of +conditions as regards temperature and surroundings. If we suppose +that the special conditions which prevail on our planet are +necessary to the highest forms of life, we still have reason to +believe that these same conditions prevail on thousands of other +worlds. The fact that we might find the conditions in millions of +other worlds unfavorable to life would not disprove the existence +of the latter on countless worlds differently situated. + +Coming down now from the general question to the specific one, we +all know that the only worlds the conditions of which can be made +the subject of observation are the planets which revolve around +the sun, and their satellites. The question whether these bodies +are inhabited is one which, of course, completely transcends not +only our powers of observation at present, but every appliance of +research that we can conceive of men devising. If Mars is +inhabited, and if the people of that planet have equal powers with +ourselves, the problem of merely producing an illumination which +could be seen in our most powerful telescope would be beyond all +the ordinary efforts of an entire nation. An unbroken square mile +of flame would be invisible in our telescopes, but a hundred +square miles might be seen. We cannot, therefore, expect to see +any signs of the works of inhabitants even on Mars. All that we +can do is to ascertain with greater or less probability whether +the conditions necessary to life exist on the other planets of the +system. + +The moon being much the nearest to us of all the heavenly bodies, +we can pronounce more definitely in its case than in any other. We +know that neither air nor water exists on the moon in quantities +sufficient to be perceived by the most delicate tests at our +command. It is certain that the moon's atmosphere, if any exists, +is less than the thousandth part of the density of that around us. +The vacuum is greater than any ordinary air-pump is capable of +producing. We can hardly suppose that so small a quantity of air +could be of any benefit whatever in sustaining life; an animal +that could get along on so little could get along on none at all. + +But the proof of the absence of life is yet stronger when we +consider the results of actual telescopic observation. An object +such as an ordinary city block could be detected on the moon. If +anything like vegetation were present on its surface, we should +see the changes which it would undergo in the course of a month, +during one portion of which it would be exposed to the rays of the +unclouded sun, and during another to the intense cold of space. If +men built cities, or even separate buildings the size of the +larger ones on our earth, we might see some signs of them. + +In recent times we not only observe the moon with the telescope, +but get still more definite information by photography. The whole +visible surface has been repeatedly photographed under the best +conditions. But no change has been established beyond question, +nor does the photograph show the slightest difference of structure +or shade which could be attributed to cities or other works of +man. To all appearances the whole surface of our satellite is as +completely devoid of life as the lava newly thrown from Vesuvius. +We next pass to the planets. Mercury, the nearest to the sun, is +in a position very unfavorable for observation from the earth, +because when nearest to us it is between us and the sun, so that +its dark hemisphere is presented to us. Nothing satisfactory has +yet been made out as to its condition. We cannot say with +certainty whether it has an atmosphere or not. What seems very +probable is that the temperature on its surface is higher than any +of our earthly animals could sustain. But this proves nothing. + +We know that Venus has an atmosphere. This was very conclusively +shown during the transits of Venus in 1874 and 1882. But this +atmosphere is so filled with clouds or vapor that it does not seem +likely that we ever get a view of the solid body of the planet +through it. Some observers have thought they could see spots on +Venus day after day, while others have disputed this view. On the +whole, if intelligent inhabitants live there, it is not likely +that they ever see sun or stars. Instead of the sun they see only +an effulgence in the vapory sky which disappears and reappears at +regular intervals. + +When we come to Mars, we have more definite knowledge, and there +seems to be greater possibilities for life there than in the case +of any other planet besides the earth. The main reason for denying +that life such as ours could exist there is that the atmosphere of +Mars is so rare that, in the light of the most recent researches, +we cannot be fully assured that it exists at all. The very careful +comparisons of the spectra of Mars and of the moon made by +Campbell at the Lick Observatory failed to show the slightest +difference in the two. If Mars had an atmosphere as dense as ours, +the result could be seen in the darkening of the lines of the +spectrum produced by the double passage of the light through it. +There were no lines in the spectrum of Mars that were not seen +with equal distinctness in that of the moon. But this does not +prove the entire absence of an atmosphere. It only shows a limit +to its density. It may be one-fifth or one-fourth the density of +that on the earth, but probably no more. + +That there must be something in the nature of vapor at least seems +to be shown by the formation and disappearance of the white polar +caps of this planet. Every reader of astronomy at the present time +knows that, during the Martian winter, white caps form around the +pole of the planet which is turned away from the sun, and grow +larger and larger until the sun begins to shine upon them, when +they gradually grow smaller, and perhaps nearly disappear. It +seems, therefore, fairly well proved that, under the influence of +cold, some white substance forms around the polar regions of Mars +which evaporates under the influence of the sun's rays. It has +been supposed that this substance is snow, produced in the same +way that snow is produced on the earth, by the evaporation of +water. + +But there are difficulties in the way of this explanation. The sun +sends less than half as much heat to Mars as to the earth, and it +does not seem likely that the polar regions can ever receive +enough of heat to melt any considerable quantity of snow. Nor does +it seem likely that any clouds from which snow could fall ever +obscure the surface of Mars. + +But a very slight change in the explanation will make it tenable. +Quite possibly the white deposits may be due to something like +hoar-frost condensed from slightly moist air, without the actual +production of snow. This would produce the effect that we see. +Even this explanation implies that Mars has air and water, rare +though the former may be. It is quite possible that air as thin as +that of Mars would sustain life in some form. Life not totally +unlike that on the earth may therefore exist upon this planet for +anything that we know to the contrary. More than this we cannot +say. + +In the case of the outer planets the answer to our question must +be in the negative. It now seems likely that Jupiter is a body +very much like our sun, only that the dark portion is too cool to +emit much, if any, light. It is doubtful whether Jupiter has +anything in the nature of a solid surface. Its interior is in all +likelihood a mass of molten matter far above a red heat, which is +surrounded by a comparatively cool, yet, to our measure, extremely +hot, vapor. The belt-like clouds which surround the planet are due +to this vapor combined with the rapid rotation. If there is any +solid surface below the atmosphere that we can see, it is swept by +winds such that nothing we have on earth could withstand them. +But, as we have said, the probabilities are very much against +there being anything like such a surface. At some great depth in +the fiery vapor there is a solid nucleus; that is all we can say. + +The planet Saturn seems to be very much like that of Jupiter in +its composition. It receives so little heat from the sun that, +unless it is a mass of fiery vapor like Jupiter, the surface must +be far below the freezing-point. + +We cannot speak with such certainty of Uranus and Neptune; yet the +probability seems to be that they are in much the same condition +as Saturn. They are known to have very dense atmospheres, which +are made known to us only by their absorbing some of the light of +the sun. But nothing is known of the composition of these +atmospheres. + +To sum up our argument: the fact that, so far as we have yet been +able to learn, only a very small proportion of the visible worlds +scattered through space are fitted to be the abode of life does +not preclude the probability that among hundreds of millions of +such worlds a vast number are so fitted. Such being the case, all +the analogies of nature lead us to believe that, whatever the +process which led to life upon this earth--whether a special act +of creative power or a gradual course of development--through that +same process does life begin in every part of the universe fitted +to sustain it. The course of development involves a gradual +improvement in living forms, which by irregular steps rise higher +and higher in the scale of being. We have every reason to believe +that this is the case wherever life exists. It is, therefore, +perfectly reasonable to suppose that beings, not only animated, +but endowed with reason, inhabit countless worlds in space. It +would, indeed, be very inspiring could we learn by actual +observation what forms of society exist throughout space, and see +the members of such societies enjoying themselves by their warm +firesides. But this, so far as we can now see, is entirely beyond +the possible reach of our race, so long as it is confined to a +single world. + + + + + +VIII + +HOW THE PLANETS ARE WEIGHED + + +You ask me how the planets are weighed? I reply, on the same +principle by which a butcher weighs a ham in a spring-balance. +When he picks the ham up, he feels a pull of the ham towards the +earth. When he hangs it on the hook, this pull is transferred from +his hand to the spring of the balance. The stronger the pull, the +farther the spring is pulled down. What he reads on the scale is +the strength of the pull. You know that this pull is simply the +attraction of the earth on the ham. But, by a universal law of +force, the ham attracts the earth exactly as much as the earth +does the ham. So what the butcher really does is to find how much +or how strongly the ham attracts the earth, and he calls that pull +the weight of the ham. On the same principle, the astronomer finds +the weight of a body by finding how strong is its attractive pull +on some other body. If the butcher, with his spring-balance and a +ham, could fly to all the planets, one after the other, weigh the +ham on each, and come back to report the results to an astronomer, +the latter could immediately compute the weight of each planet of +known diameter, as compared with that of the earth. In applying +this principle to the heavenly bodies, we at once meet a +difficulty that looks insurmountable. You cannot get up to the +heavenly bodies to do your weighing; how then will you measure +their pull? I must begin the answer to this question by explaining +a nice point in exact science. Astronomers distinguish between the +weight of a body and its mass. The weight of objects is not the +same all over the world; a thing which weighs thirty pounds in New +York would weigh an ounce more than thirty pounds in a spring- +balance in Greenland, and nearly an ounce less at the equator. +This is because the earth is not a perfect sphere, but a little +flattened. Thus weight varies with the place. If a ham weighing +thirty pounds were taken up to the moon and weighed there, the +pull would only be five pounds, because the moon is so much +smaller and lighter than the earth. There would be another weight +of the ham for the planet Mars, and yet another on the sun, where +it would weigh some eight hundred pounds. Hence the astronomer +does not speak of the weight of a planet, because that would +depend on the place where it was weighed; but he speaks of the +mass of the planet, which means how much planet there is, no +matter where you might weigh it. + +At the same time, we might, without any inexactness, agree that +the mass of a heavenly body should be fixed by the weight it would +have in New York. As we could not even imagine a planet at New +York, because it may be larger than the earth itself, what we are +to imagine is this: Suppose the planet could be divided into a +million million million equal parts, and one of these parts +brought to New York and weighed. We could easily find its weight +in pounds or tons. Then multiply this weight by a million million +million, and we shall have a weight of the planet. This would be +what the astronomers might take as the mass of the planet. + +With these explanations, let us see how the weight of the earth is +found. The principle we apply is that round bodies of the same +specific gravity attract small objects on their surface with a +force proportional to the diameter of the attracting body. For +example, a body two feet in diameter attracts twice as strongly as +one of a foot, one of three feet three times as strongly, and so +on. Now, our earth is about 40,000,000 feet in diameter; that is +10,000,000 times four feet. It follows that if we made a little +model of the earth four feet in diameter, having the average +specific gravity of the earth, it would attract a particle with +one ten-millionth part of the attraction of the earth. The +attraction of such a model has actually been measured. Since we do +not know the average specific gravity of the earth--that being in +fact what we want to find out--we take a globe of lead, four feet +in diameter, let us suppose. By means of a balance of the most +exquisite construction it is found that such a globe does exert a +minute attraction on small bodies around it, and that this +attraction is a little more than the ten-millionth part of that of +the earth. This shows that the specific gravity of the lead is a +little greater than that of the average of the whole earth. All +the minute calculations made, it is found that the earth, in order +to attract with the force it does, must be about five and one-half +times as heavy as its bulk of water, or perhaps a little more. +Different experimenters find different results; the best between +5.5 and 5.6, so that 5.5 is, perhaps, as near the number as we can +now get. This is much more than the average specific gravity of +the materials which compose that part of the earth which we can +reach by digging mines. The difference arises from the fact that, +at the depth of many miles, the matter composing the earth is +compressed into a smaller space by the enormous weight of the +portions lying above it. Thus, at the depth of 1000 miles, the +pressure on every cubic inch is more than 2000 tons, a weight +which would greatly condense the hardest metal. + +We come now to the planets. I have said that the mass or weight of +a heavenly body is determined by its attraction on some other +body. There are two ways in which the attraction of a planet may +be measured. One is by its attraction on the planets next to it. +If these bodies did not attract one another at all, but only moved +under the influence of the sun, they would move in orbits having +the form of ellipses. They are found to move very nearly in such +orbits, only the actual path deviates from an ellipse, now in one +direction and then in another, and it slowly changes its position +from year to year. These deviations are due to the pull of the +other planets, and by measuring the deviations we can determine +the amount of the pull, and hence the mass of the planet. + +The reader will readily understand that the mathematical processes +necessary to get a result in this way must be very delicate and +complicated. A much simpler method can be used in the case of +those planets which have satellites revolving round them, because +the attraction of the planet can be determined by the motions of +the satellite. The first law of motion teaches us that a body in +motion, if acted on by no force, will move in a straight line. +Hence, if we see a body moving in a curve, we know that it is +acted on by a force in the direction towards which the motion +curves. A familiar example is that of a stone thrown from the +hand. If the stone were not attracted by the earth, it would go on +forever in the line of throw, and leave the earth entirely. But +under the attraction of the earth, it is drawn down and down, as +it travels onward, until finally it reaches the ground. The faster +the stone is thrown, of course, the farther it will go, and the +greater will be the sweep of the curve of its path. If it were a +cannon-ball, the first part of the curve would be nearly a right +line. If we could fire a cannon-ball horizontally from the top of +a high mountain with a velocity of five miles a second, and if it +were not resisted by the air, the curvature of the path would be +equal to that of the surface of our earth, and so the ball would +never reach the earth, but would revolve round it like a little +satellite in an orbit of its own. Could this be done, the +astronomer would be able, knowing the velocity of the ball, to +calculate the attraction of the earth as well as we determine it +by actually observing the motion of falling bodies around us. + +Thus it is that when a planet, like Mars or Jupiter, has +satellites revolving round it, astronomers on the earth can +observe the attraction of the planet on its satellites and thus +determine its mass. The rule for doing this is very simple. The +cube of the distance between the planet and satellite is divided +by the square of the time of revolution of the satellite. The +quotient is a number which is proportional to the mass of the +planet. The rule applies to the motion of the moon round the earth +and of the planets round the sun. If we divide the cube of the +earth's distance from the sun, say 93,000,000 miles, by the square +of 365 1/4, the days in a year, we shall get a certain quotient. +Let us call this number the sun-quotient. Then, if we divide the +cube of the moon's distance from the earth by the square of its +time of revolution, we shall get another quotient, which we may +call the earth-quotient. The sun-quotient will come out about +330,000 times as large as the earth-quotient. Hence it is +concluded that the mass of the sun is 330,000 times that of the +earth; that it would take this number of earths to make a body as +heavy as the sun. + +I give this calculation to illustrate the principle; it must not +be supposed that the astronomer proceeds exactly in this way and +has only this simple calculation to make. In the case of the moon +and earth, the motion and distance of the former vary in +consequence of the attraction of the sun, so that their actual +distance apart is a changing quantity. So what the astronomer +actually does is to find the attraction of the earth by observing +the length of a pendulum which beats seconds in various latitudes. +Then, by very delicate mathematical processes, he can find with +great exactness what would be the time of revolution of a small +satellite at any given distance from the earth, and thus can get +the earth-quotient. + +But, as I have already pointed out, we must, in the case of the +planets, find the quotient in question by means of the satellites; +and it happens, fortunately, that the motions of these bodies are +much less changed by the attraction of the sun than is the motion +of the moon. Thus, when we make the computation for the outer +satellite of Mars, we find the quotient to be 1/3093500 that of +the sun-quotient. Hence we conclude that the mass of Mars is +1/3093500 that of the sun. By the corresponding quotient, the mass +of Jupiter is found to be about 1/1047 that of the sun, Saturn +1/3500, Uranus 1/22700, Neptune 1/19500. + +We have set forth only the great principle on which the astronomer +has proceeded for the purpose in question. The law of gravitation +is at the bottom of all his work. The effects of this law require +mathematical processes which it has taken two hundred years to +bring to their present state, and which are still far from +perfect. The measurement of the distance of a satellite is not a +job to be done in an evening; it requires patient labor extending +through months and years, and then is not as exact as the +astronomer would wish. He does the best he can, and must be +satisfied with that. + + + + + +IX + +THE MARINER'S COMPASS + + +Among those provisions of Nature which seem to us as especially +designed for the use of man, none is more striking than the +seeming magnetism of the earth. What would our civilization have +been if the mariner's compass had never been known? That Columbus +could never have crossed the Atlantic is certain; in what +generation since his time our continent would have been discovered +is doubtful. Did the reader ever reflect what a problem the +captain of the finest ocean liner of our day would face if he had +to cross the ocean without this little instrument? With the aid of +a pilot he gets his ship outside of Sandy Hook without much +difficulty. Even later, so long as the sun is visible and the air +is clear, he will have some apparatus for sailing by the direction +of the sun. But after a few hours clouds cover the sky. From that +moment he has not the slightest idea of east, west, north, or +south, except so far as he may infer it from the direction in +which he notices the wind to blow. For a few hours he may be +guided by the wind, provided he is sure he is not going ashore on +Long Island. Thus, in time, he feels his way out into the open +sea. By day he has some idea of direction with the aid of the sun; +by night, when the sky is clear he can steer by the Great Bear, or +"Cynosure," the compass of his ancient predecessors on the +Mediterranean. But when it is cloudy, if he persists in steaming +ahead, he may be running towards the Azores or towards Greenland, +or he may be making his way back to New York without knowing it. +So, keeping up steam only when sun or star is visible, he at +length finds that he is approaching the coast of Ireland. Then he +has to grope along much like a blind man with his staff, feeling +his way along the edge of a precipice. He can determine the +latitude at noon if the sky is clear, and his longitude in the +morning or evening in the same conditions. In this way he will get +a general idea of his whereabouts. But if he ventures to make +headway in a fog, he may find himself on the rocks at any moment. +He reaches his haven only after many spells of patient waiting for +favoring skies. + +The fact that the earth acts like a magnet, that the needle points +to the north, has been generally known to navigators for nearly a +thousand years, and is said to have been known to the Chinese at a +yet earlier period. And yet, to-day, if any professor of physical +science is asked to explain the magnetic property of the earth, he +will acknowledge his inability to do so to his own satisfaction. +Happily this does not hinder us from finding out by what law these +forces act, and how they enable us to navigate the ocean. I +therefore hope the reader will be interested in a short exposition +of the very curious and interesting laws on which the science of +magnetism is based, and which are applied in the use of the +compass. + +The force known as magnetic, on which the compass depends, is +different from all other natural forces with which we are +familiar. It is very remarkable that iron is the only substance +which can become magnetic in any considerable degree. Nickel and +one or two other metals have the same property, but in a very +slight degree. It is also remarkable that, however powerfully a +bar of steel may be magnetized, not the slightest effect of the +magnetism can be seen by its action on other than magnetic +substances. It is no heavier than before. Its magnetism does not +produce the slightest influence upon the human body. No one would +know that it was magnetic until something containing iron was +brought into its immediate neighborhood; then the attraction is +set up. The most important principle of magnetic science is that +there are two opposite kinds of magnetism, which are, in a certain +sense, contrary in their manifestations. The difference is seen in +the behavior of the magnet itself. One particular end points +north, and the other end south. What is it that distinguishes +these two ends? The answer is that one end has what we call north +magnetism, while the other has south magnetism. Every magnetic bar +has two poles, one near one end, one near the other. The north +pole is drawn towards the north pole of the earth, the south pole +towards the south pole, and thus it is that the direction of the +magnet is determined. Now, when we bring two magnets near each +other we find another curious phenomenon. If the two like poles +are brought together, they do not attract but repel each other. +But the two opposite poles attract each other. The attraction and +repulsion are exactly equal under the same conditions. There is no +more attraction than repulsion. If we seal one magnet up in a +paper or a box, and then suspend another over the box, the north +pole of the one outside will tend to the south pole of the one in +the box, and vice versa. + +Our next discovery is, that whenever a magnet attracts a piece of +iron it makes that iron into a magnet, at least for the time +being. In the case of ordinary soft or untempered iron the +magnetism disappears instantly when the magnet is removed. But if +the magnet be made to attract a piece of hardened steel, the +latter will retain the magnetism produced in it and become itself +a permanent magnet. + +This fact must have been known from the time that the compass came +into use. To make this instrument it was necessary to magnetize a +small bar or needle by passing a natural magnet over it. + +In our times the magnetization is effected by an electric current. +The latter has curious magnetic properties; a magnetic needle +brought alongside of it will be found placing itself at right +angles to the wire bearing the current. On this principle is made +the galvanometer for measuring the intensity of a current. +Moreover, if a piece of wire is coiled round a bar of steel, and a +powerful electric current pass through the coil, the bar will +become a magnet. + +Another curious property of magnetism is that we cannot develop +north magnetism in a bar without developing south magnetism at the +same time. If it were otherwise, important consequences would +result. A separate north pole of a magnet would, if attached to a +floating object and thrown into the ocean, start on a journey +towards the north all by itself. A possible method of bringing +this result about may suggest itself. Let us take an ordinary bar +magnet, with a pole at each end, and break it in the middle; then +would not the north end be all ready to start on its voyage north, +and the south end to make its way south? But, alas! when this +experiment is tried it is found that a south pole instantly +develops itself on one side of the break, and a north pole on the +other side, so that the two pieces will simply form two magnets, +each with its north and south pole. There is no possibility of +making a magnet with only one pole. + +It was formerly supposed that the central portions of the earth +consisted of an immense magnet directed north and south. Although +this view is found, for reasons which need not be set forth in +detail, to be untenable, it gives us a good general idea of the +nature of terrestrial magnetism. One result that follows from the +law of poles already mentioned is that the magnetism which seems +to belong to the north pole of the earth is what we call south on +the magnet, and vice versa. + +Careful experiment shows us that the region around every magnet is +filled with magnetic force, strongest near the poles of the +magnet, but diminishing as the inverse square of the distance from +the pole. This force, at each point, acts along a certain line, +called a line of force. These lines are very prettily shown by the +familiar experiment of placing a sheet of paper over a magnet, and +then scattering iron filings on the surface of the paper. It will +be noticed that the filings arrange themselves along a series of +curved lines, diverging in every direction from each pole, but +always passing from one pole to the other. It is a universal law +that whenever a magnet is brought into a region where this force +acts, it is attracted into such a position that it shall have the +same direction as the lines of force. Its north pole will take the +direction of the curve leading to the south pole of the other +magnet, and its south pole the opposite one. + +The fact of terrestrial magnetism may be expressed by saying that +the space within and around the whole earth is filled by lines of +magnetic force, which we know nothing about until we suspend a +magnet so perfectly balanced that it may point in any direction +whatever. Then it turns and points in the direction of the lines +of force, which may thus be mapped out for all points of the +earth. + +We commonly say that the pole of the needle points towards the +north. The poets tell us how the needle is true to the pole. Every +reader, however, is now familiar with the general fact of a +variation of the compass. On our eastern seaboard, and all the way +across the Atlantic, the north pointing of the compass varies so +far to the west that a ship going to Europe and making no +allowance for this deviation would find herself making more nearly +for the North Cape than for her destination. The "declination," as +it is termed in scientific language, varies from one region of the +earth to another. In some places it is towards the west, in others +towards the east. + +The pointing of the needle in various regions of the world is +shown by means of magnetic maps. Such maps are published by the +United States Coast Survey, whose experts make a careful study of +the magnetic force all over the country. It is found that there is +a line running nearly north and south through the Middle States +along which there is no variation of the compass. To the east of +it the variation of the north pole of the magnet is west; to the +west of it, east. The most rapid changes in the pointing of the +needle are towards the northeast and northwest regions. When we +travel to the northeastern boundary of Maine the westerly +variation has risen to 20 degrees. Towards the northwest the +easterly variation continually increases, until, in the northern +part of the State of Washington, it amounts to 23 degrees. + +When we cross the Atlantic into Europe we find the west variation +diminishing until we reach a certain line passing through central +Russia and western Asia. This is again a line of no variation. +Crossing it, the variation is once more towards the east. This +direction continues over most of the continent of Asia, but varies +in a somewhat irregular manner from one part of the continent to +another. + +As a general rule, the lines of the earth's magnetic force are not +horizontal, and therefore one end or the other of a perfectly +suspended magnet will dip below the horizontal position. This is +called the "dip of the needle." It is observed by means of a brass +circle, of which the circumference is marked off in degrees. A +magnet is attached to this circle so as to form a diameter, and +suspended on a horizontal axis passing through the centre of +gravity, so that the magnet shall be free to point in the +direction indicated by the earth's lines of magnetic force. Armed +with this apparatus, scientific travellers and navigators have +visited various points of the earth in order to determine the dip. +It is thus found that there is a belt passing around the earth +near the equator, but sometimes deviating several degrees from it, +in which there is no dip; that is to say, the lines of magnetic +force are horizontal. Taking any point on this belt and going +north, it will be found that the north pole of the magnet +gradually tends downward, the dip constantly increasing as we go +farther north. In the southern part of the United States the dip +is about 60 degrees, and the direction of the needle is nearly +perpendicular to the earth's axis. In the northern part of the +country, including the region of the Great Lakes, the dip +increases to 75 degrees. Noticing that a dip of 90 degrees would +mean that the north end of the magnet points straight downward, it +follows that it would be more nearly correct to say that, +throughout the United States, the magnetic needle points up and +down than that it points north and south. + +Going yet farther north, we find the dip still increasing, until +at a certain point in the arctic regions the north pole of the +needle points downward. In this region the compass is of no use to +the traveller or the navigator. The point is called the Magnetic +Pole. Its position has been located several times by scientific +observers. The best determinations made during the last eighty +years agree fairly well in placing it near 70 degrees north +latitude and 97 degrees longitude west from Greenwich. This point +is situated on the west shore of the Boothian Peninsula, which is +bounded on the south end by McClintock Channel. It is about five +hundred miles north of the northwest part of Hudson Bay. There is +a corresponding magnetic pole in the Antarctic Ocean, or rather on +Victoria Land, nearly south of Australia. Its position has not +been so exactly located as in the north, but it is supposed to be +at about 74 degrees of south latitude and 147 degrees of east +longitude from Greenwich. + +The magnetic poles used to be looked upon as the points towards +which the respective ends of the needle were attracted. And, as a +matter of fact, the magnetic force is stronger near the poles than +elsewhere. When located in this way by strength of force, it is +found that there is a second north pole in northern Siberia. Its +location has not, however, been so well determined as in the case +of the American pole, and it is not yet satisfactorily shown that +there is any one point in Siberia where the direction of the force +is exactly downward. + +[Illustration with caption: DIP OF THE MAGNETIC NEEDLE IN VARIOUS +LATITUDES. The arrow points show the direction of the north end of +the magnetic needle, which dips downward in north latitudes, while +the south end dips in south latitudes.] + +The declination and dip, taken together, show the exact direction +of the magnetic force at any place. But in order to complete the +statement of the force, one more element must be given--its +amount. The intensity of the magnetic force is determined by +suspending a magnet in a horizontal position, and then allowing it +to oscillate back and forth around the suspension. The stronger +the force, the less the time it will take to oscillate. Thus, by +carrying a magnet to various parts of the world, the magnetic +force can be determined at every point where a proper support for +the magnet is obtainable. The intensity thus found is called the +horizontal force. This is not really the total force, because the +latter depends upon the dip; the greater the dip, the less will be +the horizontal force which corresponds to a certain total force. +But a very simple computation enables the one to be determined +when the value of the other is known. In this way it is found +that, as a general rule, the magnetic force is least in the +earth's equatorial regions and increases as we approach either of +the magnetic poles. + +When the most exact observations on the direction of the needle +are made, it is found that it never remains at rest. Beginning +with the changes of shortest duration, we have a change which +takes place every day, and is therefore called diurnal. In our +northern latitudes it is found that during the six hours from nine +o'clock at night until three in the morning the direction of the +magnet remains nearly the same. But between three and four A.M. it +begins to deviate towards the east, going farther and farther east +until about 8 A.M. Then, rather suddenly, it begins to swing +towards the west with a much more rapid movement, which comes to +an end between one and two o'clock in the afternoon. Then, more +slowly, it returns in an easterly direction until about nine at +night, when it becomes once more nearly quiescent. Happily, the +amount of this change is so small that the navigator need not +trouble himself with it. The entire range of movement rarely +amounts to one-quarter of a degree. + +It is a curious fact that the amount of the change is twice as +great in June as it is in December. This indicates that it is +caused by the sun's radiation. But how or why this cause should +produce such an effect no one has yet discovered. + +Another curious feature is that in the southern hemisphere the +direction of the motion is reversed, although its general +character remains the same. The pointing deviates towards the west +in the morning, then rapidly moves towards the east until about +two o'clock, after which it slowly returns to its original +direction. + +The dip of the needle goes through a similar cycle of daily +changes. In northern latitudes it is found that at about six in +the morning the dip begins to increase, and continues to do so +until noon, after which it diminishes until seven or eight o'clock +in the evening, when it becomes nearly constant for the rest of +the night. In the southern hemisphere the direction of the +movement is reversed. + +When the pointing of the needle is compared with the direction of +the moon, it is found that there is a similar change. But, instead +of following the moon in its course, it goes through two periods +in a day, like the tides. When the moon is on the meridian, +whether above or below us, the effect is in one direction, while +when it is rising or setting it is in the opposite direction. In +other words, there is a complete swinging backward and forward +twice in a lunar day. It might be supposed that such an effect +would be due to the moon, like the earth, being a magnet. But were +this the case there would be only one swing back and forth during +the passage of the moon from the meridian until it came back to +the meridian again. The effect would be opposite at the rising and +setting of the moon, which we have seen is not the case. To make +the explanation yet more difficult, it is found that, as in the +case of the sun, the change is opposite in the northern and +southern hemispheres and very small at the equator, where, by +virtue of any action that we can conceive of, it ought to be +greatest. The pointing is also found to change with the age of the +moon and with the season of the year. But these motions are too +small to be set forth in the present article. + +There is yet another class of changes much wider than these. The +observations recorded since the time of Columbus show that, in the +course of centuries, the variation of the compass, at any one +point, changes very widely. It is well known that in 1490 the +needle pointed east of north in the Mediterranean, as well as in +those portions of the Atlantic which were then navigated. Columbus +was therefore much astonished when, on his first voyage, in mid- +ocean, he found that the deviation was reversed, and was now +towards the west. It follows that a line of no variation then +passed through the Atlantic Ocean. But this line has since been +moving towards the east. About 1662 it passed the meridian of +Paris. During the two hundred and forty years which have since +elapsed, it has passed over Central Europe, and now, as we have +already said, passes through European Russia. + +The existence of natural magnets composed of iron ore, and their +property of attracting iron and making it magnetic, have been +known from the remotest antiquity. But the question as to who +first discovered the fact that a magnetized needle points north +and south, and applied this discovery to navigation, has given +rise to much discussion. That the property was known to the +Chinese about the beginning of our era seems to be fairly well +established, the statements to that effect being of a kind that +could not well have been invented. Historical evidence of the use +of the magnetic needle in navigation dates from the twelfth +century. The earliest compass consisted simply of a splinter of +wood or a piece of straw to which the magnetized needle was +attached, and which was floated in water. A curious obstacle is +said to have interfered with the first uses of this instrument. +Jack is a superstitious fellow, and we may be sure that he was not +less so in former times than he is today. From his point of view +there was something uncanny in so very simple a contrivance as a +floating straw persistently showing him the direction in which he +must sail. It made him very uncomfortable to go to sea under the +guidance of an invisible power. But with him, as with the rest of +us, familiarity breeds contempt, and it did not take more than a +generation to show that much good and no harm came to those who +used the magic pointer. + +The modern compass, as made in the most approved form for naval +and other large ships, is the liquid one. This does not mean that +the card bearing the needle floats on the liquid, but only that a +part of the force is taken off from the pivot on which it turns, +so as to make the friction as small as possible, and to prevent +the oscillation back and forth which would continually go on if +the card were perfectly free to turn. The compass-card is marked +not only with the thirty-two familiar points of the compass, but +is also divided into degrees. In the most accurate navigation it +is probable that very little use of the points is made, the ship +being directed according to the degrees. + +A single needle is not relied upon to secure the direction of the +card, the latter being attached to a system of four or even more +magnets, all pointing in the same direction. The compass must have +no iron in its construction or support, because the attraction of +that substance on the needle would be fatal to its performance. + +From this cause the use of iron as ship-building material +introduced a difficulty which it was feared would prove very +serious. The thousands of tons of iron in a ship must exert a +strong attraction on the magnetic needle. Another complication is +introduced by the fact that the iron of the ship will always +become more or less magnetic, and when the ship is built of steel, +as modern ones are, this magnetism will be more or less permanent. + +We have already said that a magnet has the property of making +steel or iron in its neighborhood into another magnet, with its +poles pointing in the opposite direction. The consequence is that +the magnetism of the earth itself will make iron or steel more or +less magnetic. As a ship is built she thus becomes a great +repository of magnetism, the direction of the force of which will +depend upon the position in which she lay while building. If +erected on the bank of an east and west stream, the north end of +the ship will become the north pole of a magnet and the south end +the south pole. Accordingly, when she is launched and proceeds to +sea, the compass points not exactly according to the magnetism of +the earth, but partly according to that of the ship also. + +The methods of obviating this difficulty have exercised the +ingenuity of the ablest physicists from the beginning of iron ship +building. One method is to place in the neighborhood of the +compass, but not too near it, a steel bar magnetized in the +opposite direction from that of the ship, so that the action of +the latter shall be neutralized. But a perfect neutralization +cannot be thus effected. It is all the more difficult to effect it +because the magnetism of a ship is liable to change. + +The practical method therefore adopted is called "swinging the +ship," an operation which passengers on ocean liners may have +frequently noticed when approaching land. The ship is swung around +so that her bow shall point in various directions. At each +pointing the direction of the ship is noticed by sighting on the +sun, and also the direction of the compass itself. In this way the +error of the pointing of the compass as the ship swings around is +found for every direction in which she may be sailing. A table can +then be made showing what the pointing, according to the compass, +should be in order that the ship may sail in any given direction. + +This, however, does not wholly avoid the danger. The tables thus +made are good when the ship is on a level keel. If, from any cause +whatever, she heels over to one side, the action will be +different. Thus there is a "heeling error" which must be allowed +for. It is supposed to have been from this source of error not +having been sufficiently determined or appreciated that the +lamentable wreck of the United States ship Huron off the coast of +Hatteras occurred some twenty years ago. + + + + + +X + +THE FAIRYLAND OF GEOMETRY + + +If the reader were asked in what branch of science the imagination +is confined within the strictest limits, he would, I fancy, reply +that it must be that of mathematics. The pursuer of this science +deals only with problems requiring the most exact statements and +the most rigorous reasoning. In all other fields of thought more +or less room for play may be allowed to the imagination, but here +it is fettered by iron rules, expressed in the most rigid logical +form, from which no deviation can be allowed. We are told by +philosophers that absolute certainty is unattainable in all +ordinary human affairs, the only field in which it is reached +being that of geometric demonstration. + +And yet geometry itself has its fairyland--a land in which the +imagination, while adhering to the forms of the strictest +demonstration, roams farther than it ever did in the dreams of +Grimm or Andersen. One thing which gives this field its strictly +mathematical character is that it was discovered and explored in +the search after something to supply an actual want of +mathematical science, and was incited by this want rather than by +any desire to give play to fancy. Geometricians have always sought +to found their science on the most logical basis possible, and +thus have carefully and critically inquired into its foundations. +The new geometry which has thus arisen is of two closely related +yet distinct forms. One of these is called NON-EUCLIDIAN, because +Euclid's axiom of parallels, which we shall presently explain, is +ignored. In the other form space is assumed to have one or more +dimensions in addition to the three to which the space we actually +inhabit is confined. As we go beyond the limits set by Euclid in +adding a fourth dimension to space, this last branch as well as +the other is often designated non-Euclidian. But the more common +term is hypergeometry, which, though belonging more especially to +space of more than three dimensions, is also sometimes applied to +any geometric system which transcends our ordinary ideas. + +In all geometric reasoning some propositions are necessarily taken +for granted. These are called axioms, and are commonly regarded as +self-evident. Yet their vital principle is not so much that of +being self-evident as being, from the nature of the case, +incapable of demonstration. Our edifice must have some support to +rest upon, and we take these axioms as its foundation. One example +of such a geometric axiom is that only one straight line can be +drawn between two fixed points; in other words, two straight lines +can never intersect in more than a single point. The axiom with +which we are at present concerned is commonly known as the 11th of +Euclid, and may be set forth in the following way: We have given a +straight line, A B, and a point, P, with another line, C D, +passing through it and capable of being turned around on P. Euclid +assumes that this line C D will have one position in which it will +be parallel to A B, that is, a position such that if the two lines +are produced without end, they will never meet. His axiom is that +only one such line can be drawn through P. That is to say, if we +make the slightest possible change in the direction of the line C +D, it will intersect the other line, either in one direction or +the other. + +The new geometry grew out of the feeling that this proposition +ought to be proved rather than taken as an axiom; in fact, that it +could in some way be derived from the other axioms. Many +demonstrations of it were attempted, but it was always found, on +critical examination, that the proposition itself, or its +equivalent, had slyly worked itself in as part of the base of the +reasoning, so that the very thing to be proved was really taken +for granted. + +[Illustration with caption: FIG. I] + +This suggested another course of inquiry. If this axiom of +parallels does not follow from the other axioms, then from these +latter we may construct a system of geometry in which the axiom of +parallels shall not be true. This was done by Lobatchewsky and +Bolyai, the one a Russian the other a Hungarian geometer, about +1830. + +To show how a result which looks absurd, and is really +inconceivable by us, can be treated as possible in geometry, we +must have recourse to analogy. Suppose a world consisting of a +boundless flat plane to be inhabited by reasoning beings who can +move about at pleasure on the plane, but are not able to turn +their heads up or down, or even to see or think of such terms as +above them and below them, and things around them can be pushed or +pulled about in any direction, but cannot be lifted up. People and +things can pass around each other, but cannot step over anything. +These dwellers in "flatland" could construct a plane geometry +which would be exactly like ours in being based on the axioms of +Euclid. Two parallel straight lines would never meet, though +continued indefinitely. + +But suppose that the surface on which these beings live, instead +of being an infinitely extended plane, is really the surface of an +immense globe, like the earth on which we live. It needs no +knowledge of geometry, but only an examination of any globular +object--an apple, for example--to show that if we draw a line as +straight as possible on a sphere, and parallel to it draw a small +piece of a second line, and continue this in as straight a line as +we can, the two lines will meet when we proceed in either +direction one-quarter of the way around the sphere. For our "flat- +land" people these lines would both be perfectly straight, because +the only curvature would be in the direction downward, which they +could never either perceive or discover. The lines would also +correspond to the definition of straight lines, because any +portion of either contained between two of its points would be the +shortest distance between those points. And yet, if these people +should extend their measures far enough, they would find any two +parallel lines to meet in two points in opposite directions. For +all small spaces the axioms of their geometry would apparently +hold good, but when they came to spaces as immense as the semi- +diameter of the earth, they would find the seemingly absurd result +that two parallel lines would, in the course of thousands of +miles, come together. Another result yet more astonishing would be +that, going ahead far enough in a straight line, they would find +that although they had been going forward all the time in what +seemed to them the same direction, they would at the end of 25,000 +miles find themselves once more at their starting-point. + +One form of the modern non-Euclidian geometry assumes that a +similar theorem is true for the space in which our universe is +contained. Although two straight lines, when continued +indefinitely, do not appear to converge even at the immense +distances which separate us from the fixed stars, it is possible +that there may be a point at which they would eventually meet +without either line having deviated from its primitive direction +as we understand the case. It would follow that, if we could start +out from the earth and fly through space in a perfectly straight +line with a velocity perhaps millions of times that of light, we +might at length find ourselves approaching the earth from a +direction the opposite of that in which we started. Our straight- +line circle would be complete. + +Another result of the theory is that, if it be true, space, though +still unbounded, is not infinite, just as the surface of a sphere, +though without any edge or boundary, has only a limited extent of +surface. Space would then have only a certain volume--a volume +which, though perhaps greater than that of all the atoms in the +material universe, would still be capable of being expressed in +cubic miles. If we imagine our earth to grow larger and larger in +every direction without limit, and with a speed similar to that we +have described, so that to-morrow it was large enough to extend to +the nearest fixed stars, the day after to yet farther stars, and +so on, and we, living upon it, looked out for the result, we +should, in time, see the other side of the earth above us, coming +down upon us? as it were. The space intervening would grow +smaller, at last being filled up. The earth would then be so +expanded as to fill all existing space. + +This, although to us the most interesting form of the non- +Euclidian geometry, is not the only one. The idea which +Lobatchewsky worked out was that through a point more than one +parallel to a given line could be drawn; that is to say, if +through the point P we have already supposed another line were +drawn making ever so small an angle with CD, this line also would +never meet the line AB. It might approach the latter at first, but +would eventually diverge. The two lines AB and CD, starting +parallel, would eventually, perhaps at distances greater than that +of the fixed stars, gradually diverge from each other. This system +does not admit of being shown by analogy so easily as the other, +but an idea of it may be had by supposing that the surface of +"flat-land," instead of being spherical, is saddle-shaped. +Apparently straight parallel lines drawn upon it would then +diverge, as supposed by Bolyai. We cannot, however, imagine such a +surface extended indefinitely without losing its properties. The +analogy is not so clearly marked as in the other case. + +To explain hypergeometry proper we must first set forth what a +fourth dimension of space means, and show how natural the way is +by which it may be approached. We continue our analogy from "flat- +land" In this supposed land let us make a cross--two straight +lines intersecting at right angles. The inhabitants of this land +understand the cross perfectly, and conceive of it just as we do. +But let us ask them to draw a third line, intersecting in the same +point, and perpendicular to both the other lines. They would at +once pronounce this absurd and impossible. It is equally absurd +and impossible to us if we require the third line to be drawn on +the paper. But we should reply, "If you allow us to leave the +paper or flat surface, then we can solve the problem by simply +drawing the third line through the paper perpendicular to its +surface." + +[Illustration with caption: FIG. 2] + +Now, to pursue the analogy, suppose that, after we have drawn +three mutually perpendicular lines, some being from another sphere +proposes to us the drawing of a fourth line through the same +point, perpendicular to all three of the lines already there. We +should answer him in the same way that the inhabitants of "flat- +land" answered us: "The problem is impossible. You cannot draw any +such line in space as we understand it." If our visitor conceived +of the fourth dimension, he would reply to us as we replied to the +"flat-land" people: "The problem is absurd and impossible if you +confine your line to space as you understand it. But for me there +is a fourth dimension in space. Draw your line through that +dimension, and the problem will be solved. This is perfectly +simple to me; it is impossible to you solely because your +conceptions do not admit of more than three dimensions." + +Supposing the inhabitants of "flat-land" to be intellectual beings +as we are, it would be interesting to them to be told what +dwellers of space in three dimensions could do. Let us pursue the +analogy by showing what dwellers in four dimensions might do. +Place a dweller of "flat-land" inside a circle drawn on his plane, +and ask him to step outside of it without breaking through it. He +would go all around, and, finding every inch of it closed, he +would say it was impossible from the very nature of the +conditions. "But," we would reply, "that is because of your +limited conceptions. We can step over it." + +"Step over it!" he would exclaim. "I do not know what that means. +I can pass around anything if there is a way open, but I cannot +imagine what you mean by stepping over it." + +But we should simply step over the line and reappear on the other +side. So, if we confine a being able to move in a fourth dimension +in the walls of a dungeon of which the sides, the floor, and the +ceiling were all impenetrable, he would step outside of it without +touching any part of the building, just as easily as we could step +over a circle drawn on the plane without touching it. He would +simply disappear from our view like a spirit, and perhaps reappear +the next moment outside the prison. To do this he would only have +to make a little excursion in the fourth dimension. + +[Illustration with caption: FIG. 3] + +Another curious application of the principle is more purely +geometrical. We have here two triangles, of which the sides and +angles of the one are all equal to corresponding sides and angles +of the other. Euclid takes it for granted that the one triangle +can be laid upon the other so that the two shall fit together. But +this cannot be done unless we lift one up and turn it over. In the +geometry of "flat-land" such a thing as lifting up is +inconceivable; the two triangles could never be fitted together. + +[Illustration with caption: FIG 4] + +Now let us suppose two pyramids similarly related. All the faces +and angles of the one correspond to the faces and angles of the +other. Yet, lift them about as we please, we could never fit them +together. If we fit the bases together the two will lie on +opposite sides, one being below the other. But the dweller in four +dimensions of space will fit them together without any trouble. By +the mere turning over of one he will convert it into the other +without any change whatever in the relative position of its parts. +What he could do with the pyramids he could also do with one of us +if we allowed him to take hold of us and turn a somersault with us +in the fourth dimension. We should then come back into our natural +space, but changed as if we were seen in a mirror. Everything on +us would be changed from right to left, even the seams in our +clothes, and every hair on our head. All this would be done +without, during any of the motion, any change having occurred in +the positions of the parts of the body. + +It is very curious that, in these transcendental speculations, the +most rigorous mathematical methods correspond to the most +mystical ideas of the Swedenborgian and other forms of religion. +Right around us, but in a direction which we cannot conceive any +more than the inhabitants of "flat-land" can conceive up and down, +there may exist not merely another universe, but any number of +universes. All that physical science can say against the +supposition is that, even if a fourth dimension exists, there is +some law of all the matter with which we are acquainted which +prevents any of it from entering that dimension, so that, in our +natural condition, it must forever remain unknown to us. + +Another possibility in space of four dimensions would be that of +turning a hollow sphere, an india-rubber ball, for example, inside +out by simple bending without tearing it. To show the motion in +our space to which this is analogous, let us take a thin, round +sheet of india-rubber, and cut out all the central part, leaving +only a narrow ring round the border. Suppose the outer edge of +this ring fastened down on a table, while we take hold of the +inner edge and stretch it upward and outward over the outer edge +until we flatten the whole ring on the table, upside down, with +the inner edge now the outer one. This motion would be as +inconceivable in "flat-land" as turning the ball inside out is to +us. + + + + + +XI + +THE ORGANIZATION OF SCIENTIFIC RESEARCH + + +The claims of scientific research on the public were never more +forcibly urged than in Professor Ray Lankester's recent Romanes +Lecture before the University of Oxford. Man is here eloquently +pictured as Nature's rebel, who, under conditions where his great +superior commands "Thou shalt die," replies "I will live." In +pursuance of this determination, civilized man has proceeded so +far in his interference with the regular course of Nature that he +must either go on and acquire firmer control of the conditions, or +perish miserably by the vengeance certain to be inflicted on the +half-hearted meddler in great affairs. This rebel by every step +forward renders himself liable to greater and greater penalties, +and so cannot afford to pause or fail in one single step. One of +Nature's most powerful agencies in thwarting his determination to +live is found in disease-producing parasites. "Where there is one +man of first-rate intelligence now employed in gaining knowledge +of this agency, there should be a thousand. It should be as much +the purpose of civilized nations to protect their citizens in this +respect as it is to provide defence against human aggression." + +It was no part of the function of the lecturer to devise a plan +for carrying on the great war he proposes to wage. The object of +the present article is to contribute some suggestions in this +direction; with especial reference to conditions in our own +country; and no better text can be found for a discourse on the +subject than the preceding quotation. In saying that there should +be a thousand investigators of disease where there is now one, I +believe that Professor Lankester would be the first to admit that +this statement was that of an ideal to be aimed at, rather than of +an end to be practically reached. Every careful thinker will agree +that to gather a body of men, young or old, supply them with +laboratories and microscopes, and tell them to investigate +disease, would be much like sending out an army without trained +leaders to invade an enemy's country. + +There is at least one condition of success in this line which is +better fulfilled in our own country than in any other; and that is +liberality of support on the part of munificent citizens desirous +of so employing their wealth as to promote the public good. +Combining this instrumentality with the general public spirit of +our people, it must be admitted that, with all the disadvantages +under which scientific research among us has hitherto labored, +there is still no country to which we can look more hopefully than +to our own as the field in which the ideal set forth by Professor +Lankester is to be pursued. Some thoughts on the question how +scientific research may be most effectively promoted in our own +country through organized effort may therefore be of interest. Our +first step will be to inquire what general lessons are to be +learned from the experience of the past. + +The first and most important of these lessons is that research has +never reached its highest development except at centres where +bodies of men engaged in it have been brought together, and +stimulated to action by mutual sympathy and support. We must call +to mind that, although the beginnings of modern science were laid +by such men as Copernicus, Galileo, Leonardo da Vinci, and +Torricelli, before the middle of the seventeenth century, unbroken +activity and progress date from the foundations of the Academy of +Sciences of Paris and the Royal Society of London at that time. +The historic fact that the bringing of men together, and their +support by an intelligent and interested community, is the first +requirement to be kept in view can easily be explained. Effective +research involves so intricate a network of problems and +considerations that no one engaged in it can fail to profit by the +suggestions of kindred spirits, even if less acquainted with the +subject than he is himself. Intelligent discussion suggests new +ideas and continually carries the mind to a higher level of +thought. We must not regard the typical scientific worker, even of +the highest class, as one who, having chosen his special field and +met with success in cultivating it, has only to be supplied with +the facilities he may be supposed to need in order to continue his +work in the most efficient way. What we have to deal with is not a +fixed and permanent body of learned men, each knowing all about +the field of work in which he is engaged, but a changing and +growing class, constantly recruited by beginners at the bottom of +the scale, and constantly depleted by the old dropping away at the +top. No view of the subject is complete which does not embrace the +entire activity of the investigator, from the tyro to the leader. +The leader himself, unless engaged in the prosecution of some +narrow specialty, can rarely be so completely acquainted with his +field as not to need information from others. Without this, he is +constantly liable to be repeating what has already been better +done than he can do it himself, of following lines which are known +to lead to no result, and of adopting methods shown by the +experience of others not to be the best. Even the books and +published researches to which he must have access may be so +voluminous that he cannot find time to completely examine them for +himself; or they may be inaccessible. All this will make it clear +that, with an occasional exception, the best results of research +are not to be expected except at centres where large bodies of men +are brought into close personal contact. + +In addition to the power and facility acquired by frequent +discussion with his fellows, the appreciation and support of an +intelligent community, to whom the investigator may, from time to +time, make known his thoughts and the results of his work, add a +most effective stimulus. The greater the number of men of like +minds that can be brought together and the larger the community +which interests itself in what they are doing, the more rapid will +be the advance and the more effective the work carried on. It is +thus that London, with its munificently supported institutions, +and Paris and Berlin, with their bodies of investigators supported +either by the government or by various foundations, have been for +more than three centuries the great centres where we find +scientific activity most active and most effective. Looking at +this undoubted fact, which has asserted itself through so long a +period, and which asserts itself today more strongly than ever, +the writer conceives that there can be no question as to one +proposition. If we aim at the single object of promoting the +advance of knowledge in the most effective way, and making our own +country the leading one in research, our efforts should be +directed towards bringing together as many scientific workers as +possible at a single centre, where they can profit in the highest +degree by mutual help, support, and sympathy. + +In thus strongly setting forth what must seem an indisputable +conclusion, the writer does not deny that there are drawbacks to +such a policy, as there are to every policy that can be devised +aiming at a good result. Nature offers to society no good that she +does not accompany by a greater or less measure of evil The only +question is whether the good outweighs the evil. In the present +case, the seeming evil, whether real or not, is that of +centralization. A policy tending in this direction is held to be +contrary to the best interests of science in quarters entitled to +so much respect that we must inquire into the soundness of the +objection. + +It would be idle to discuss so extreme a question as whether we +shall take all the best scientific investigators of our country +from their several seats of learning and attract them to some one +point. We know that this cannot be done, even were it granted that +success would be productive of great results. The most that can be +done is to choose some existing centre of learning, population, +wealth, and influence, and do what we can to foster the growth of +science at that centre by attracting thither the greatest possible +number of scientific investigators, especially of the younger +class, and making it possible for them to pursue their researches +in the most effective way. This policy would not result in the +slightest harm to any institution or community situated elsewhere. +It would not be even like building up a university to outrank all +the others of our country; because the functions of the new +institution, if such should be founded, would in its relations to +the country be radically different from those of a university. Its +primary object would not be the education of youth, but the +increase of knowledge. So far as the interests of any community or +of the world at large are concerned, it is quite indifferent where +knowledge may be acquired, because, when once acquired and made +public, it is free to the world. The drawbacks suffered by other +centres would be no greater than those suffered by our Western +cities, because all the great departments of the government are +situated at a single distant point. Strong arguments could +doubtless be made for locating some of these departments in the +Far West, in the Mississippi Valley, or in various cities of the +Atlantic coast; but every one knows that any local advantages thus +gained would be of no importance compared with the loss of that +administrative efficiency which is essential to the whole country. + +There is, therefore, no real danger from centralization. The +actual danger is rather in the opposite direction; that the +sentiment against concentrating research will prove to operate too +strongly. There is a feeling that it is rather better to leave +every investigator where he chances to be at the moment, a feeling +which sometimes finds expression in the apothegm that we cannot +transplant a genius. That such a proposition should find +acceptance affords a striking example of the readiness of men to +accept a euphonious phrase without inquiring whether the facts +support the doctrine which it enunciates. The fact is that many, +perhaps the majority, of the great scientific investigators of +this and of former times have done their best work through being +transplanted. As soon as the enlightened monarchs of Europe felt +the importance of making their capitals great centres of learning, +they began to invite eminent men of other countries to their own. +Lagrange was an Italian transplanted to Paris, as a member of the +Academy of Sciences, after he had shown his powers in his native +country. His great contemporary, Euler, was a Swiss, transplanted +first to St. Petersburg, then invited by Frederick the Great to +become a member of the Berlin Academy, then again attracted to St. +Petersburg. Huyghens was transplanted from his native country to +Paris. Agassiz was an exotic, brought among us from Switzerland, +whose activity during the generation he passed among us was as +great and effective as at any time of his life. On the Continent, +outside of France, the most eminent professors in the universities +have been and still are brought from distant points. So numerous +are the cases of which these are examples that it would be more in +accord with the facts to claim that it is only by transplanting a +genius that we stimulate him to his best work. + +Having shown that the best results can be expected only by +bringing into contact as many scientific investigators as +possible, the next question which arises is that of their +relations to one another. It may be asked whether we shall aim at +individualism or collectivism. Shall our ideal be an organized +system of directors, professors, associates, assistants, fellows; +or shall it be a collection of individual workers, each pursuing +his own task in the way he deems best, untrammelled by authority? + +The reply to this question is that there is in this special case +no antagonism between the two ideas. The most effective +organization will aim both at the promotion of individual effort, +and at subordination and co-operation. It would be a serious error +to formulate any general rule by which all cases should be +governed. The experience of the past should be our guide, so far +as it applies to present and future conditions; but in availing +ourselves of it we must remember that conditions are constantly +changing, and must adapt our policy to the problems of the future. +In doing this, we shall find that different fields of research +require very different policies as regards co-operation and +subordination. It will be profitable to point out those special +differences, because we shall thereby gain a more luminous insight +into the problems which now confront the scientific investigator, +and better appreciate their variety, and the necessity of +different methods of dealing with them. + +At one extreme, we have the field of normative science, work in +which is of necessity that of the individual mind alone. This +embraces pure mathematics and the methods of science in their +widest range. The common interests of science require that these +methods shall be worked out and formulated for the guidance of +investigators generally, and this work is necessarily that of the +individual brain. + +At the other extreme, we have the great and growing body of +sciences of observation. Through the whole nineteenth century, to +say nothing of previous centuries, organizations, and even +individuals, have been engaged in recording the innumerable phases +of the course of nature, hoping to accumulate material that +posterity shall be able to utilize for its benefit. We have +observations astronomical, meteorological, magnetic, and social, +accumulating in constantly increasing volume, the mass of which is +so unmanageable with our present organizations that the question +might well arise whether almost the whole of it will not have to +be consigned to oblivion. Such a conclusion should not be +entertained until we have made a vigorous effort to find what pure +metal of value can be extracted from the mass of ore. To do this +requires the co-operation of minds of various orders, quite akin +in their relations to those necessary in a mine or great +manufacturing establishment. Laborers whose duties are in a large +measure matters of routine must be guided by the skill of a class +higher in quality and smaller in number than their own, and these +again by the technical knowledge of leaders in research. Between +these extremes we have a great variety of systems of co-operation. + +There is another feature of modern research the apprehension of +which is necessary to the completeness of our view. A cursory +survey of the field of science conveys the impression that it +embraces only a constantly increasing number of disconnected +specialties, in which each cultivator knows little or nothing of +what is being done by others. Measured by its bulk, the published +mass of scientific research is increasing in a more than +geometrical ratio. Not only do the publications of nearly every +scientific society increase in number and volume, but new and +vigorous societies are constantly organized to add to the sum +total. The stately quartos issued from the presses of the leading +academies of Europe are, in most cases, to be counted by hundreds. +The Philosophical Transactions of the Royal Society already number +about two hundred volumes, and the time when the Memoirs of the +French Academy of Sciences shall reach the thousand mark does not +belong to the very remote future. Besides such large volumes, +these and other societies publish smaller ones in a constantly +growing number. In addition to the publications of learned +societies, there are journals devoted to each scientific +specialty, which seem to propagate their species by subdivision in +much the same way as some of the lower orders of animal life. +Every new publication of the kind is suggested by the wants of a +body of specialists, who require a new medium for their researches +and communications. The time has already come when we cannot +assume that any specialist is acquainted with all that is being +done even in his own line. To keep the run of this may well be +beyond his own powers; more he can rarely attempt. + +What is the science of the future to do when this huge mass +outgrows the space that can be found for it in the libraries, and +what are we to say of the value of it all? Are all these +scientific researches to be classed as really valuable +contributions to knowledge, or have we only a pile in which +nuggets of gold are here and there to be sought for? One +encouraging answer to such a question is that, taking the +interests of the world as a whole, scientific investigation has +paid for itself in benefits to humanity a thousand times over, and +that all that is known to-day is but an insignificant fraction of +what Nature has to show us. Apart from this, another feature of +the science of our time demands attention. While we cannot hope +that the multiplication of specialties will cease, we find that +upon the process of differentiation and subdivision is now being +superposed a form of evolution, tending towards the general unity +of all the sciences, of which some examples may be pointed out. + +Biological science, which a generation ago was supposed to be at +the antipodes of exact science, is becoming more and more exact, +and is cultivated by methods which are developed and taught by +mathematicians. Psychophysics--the study of the operations of the +mind by physical apparatus of the same general nature as that used +by the chemist and physicist--is now an established branch of +research. A natural science which, if any comparisons are +possible, may outweigh all others in importance to the race, is +the rising one of "eugenics,"--the improvement of the human race +by controlling the production of its offspring. No better example +of the drawbacks which our country suffers as a seat of science +can be given than the fact that the beginning of such a science +has been possible only at the seat of a larger body of cultivated +men than our land has yet been able to bring together. Generations +may elapse before the seed sown by Mr. Francis Galton, from which +grew the Eugenic Society, shall bear full fruit in the adoption of +those individual efforts and social regulations necessary to the +propagation of sound and healthy offspring on the part of the +human family. But when this comes about, then indeed will +Professor Lankester's "rebel against Nature" find his independence +acknowledged by the hitherto merciless despot that has decreed +punishment for his treason. + +This new branch of science from which so much may be expected is +the offshoot of another, the rapid growth of which illustrates the +rapid invasion of the most important fields of thought by the +methods of exact science. It is only a few years since it was +remarked of Professor Karl Pearson's mathematical investigations +into the laws of heredity, and the biological questions associated +with these laws, that he was working almost alone, because the +biologists did not understand his mathematics, while the +mathematicians were not interested in his biology. Had he not +lived at a great centre of active thought, within the sphere of +influence of the two great universities of England, it is quite +likely that this condition of isolation would have been his to the +end. But, one by one, men were found possessing the skill and +interest in the subject necessary to unite in his work, which now +has not only a journal of its own, but is growing in a way which, +though slow, has all the marks of healthy progress towards an end +the importance of which has scarcely dawned upon the public mind. + +Admitting that an organized association of investigators is of the +first necessity to secure the best results in the scientific work +of the future, we meet the question of the conditions and auspices +under which they are to be brought together. The first thought to +strike us at this point may well be that we have, in our great +universities, organizations which include most of the leading men +now engaged in scientific research, whose personnel and facilities +we should utilize. Admitting, as we all do, that there are already +too many universities, and that better work would be done by a +consolidation of the smaller ones, a natural conclusion is that +the end in view will be best reached through existing +organizations. But it would be a great mistake to jump at this +conclusion without a careful study of the conditions. The brief +argument--there are already too many institutions--instead of +having more we should strengthen those we have--should not be +accepted without examination. Had it been accepted thirty years +ago, there are at least two great American universities of to-day +which would not have come into being, the means devoted to their +support having been divided among others. These are the Johns +Hopkins and the University of Chicago. What would have been gained +by applying the argument in these cases? The advantage would have +been that, instead of 146 so-called universities which appear to- +day in the Annual Report of the Bureau of Education, we should +have had only 144. The work of these 144 would have been +strengthened by an addition, to their resources, represented by +the endowments of Baltimore and Chicago, and sufficient to add +perhaps one professor to the staff of each. Would the result have +been better than it actually has been? Have we not gained anything +by allowing the argument to be forgotten in the cases of these two +institutions? I do not believe that any who carefully look at the +subject will hesitate in answering this question in the +affirmative. The essential point is that the Johns Hopkins +University did not merely add one to an already overcrowded list, +but that it undertook a mission which none of the others was then +adequately carrying out. If it did not plant the university idea +in American soil, it at least gave it an impetus which has now +made it the dominant one in the higher education of almost every +state. + +The question whether the country at large would have reaped a +greater benefit, had the professors of the University of Chicago, +with the appliances they now command, been distributed among fifty +or a hundred institutions in every quarter of the land, than it +has actually reaped from that university, is one which answers +itself. Our two youngest universities have attained success, not +because two have thus been added to the number of American +institutions of learning, but because they had a special mission, +required by the advance of the age, for which existing +institutions were inadequate. + +The conclusion to which these considerations lead is simple. No +new institution is needed to pursue work on traditional lines, +guided by traditional ideas. But, if a new idea is to be +vigorously prosecuted, then a young and vigorous institution, +specially organized to put the idea into effect, is necessary. The +project of building up in our midst, at the most appropriate +point, an organization of leading scientific investigators, for +the single purpose of giving a new impetus to American science +and, if possible, elevating the thought of the country and of the +world to a higher plane, involves a new idea, which can best be +realized by an institution organized for the special purpose. +While this purpose is quite in line with that of the leading +universities, it goes too far beyond them to admit of its complete +attainment through their instrumentality. The first object of a +university is the training of the growing individual for the +highest duties of life. Additions to the mass of knowledge have +not been its principal function, nor even an important function in +our own country, until a recent time. The primary object of the +proposed institution is the advance of knowledge and the opening +up of new lines of thought, which, it may be hoped, are to prove +of great import to humanity. It does not follow that the function +of teaching shall be wholly foreign to its activities. It must +take up the best young men at the point where universities leave +them, and train them in the arts of thinking and investigating. +But this training will be beyond that which any regular university +is carrying out. + +In pursuing our theme the question next arises as to the special +features of the proposed association. The leading requirement is +one that cannot be too highly emphasized. How clearly soever the +organizers may have in their minds' eye the end in view, they must +recognize the fact that it cannot be attained in a day. In every +branch of work which is undertaken, there must be a single leader, +and he must be the best that the country, perhaps even the world, +can produce. The required man is not to be found without careful +inquiry; in many branches he may be unattainable for years. When +such is the case, wait patiently till he appears. Prudence +requires that the fewest possible risks would be taken, and that +no leader should be chosen except one of tried experience and +world-wide reputation. Yet we should not leave wholly out of sight +the success of the Johns Hopkins University in selecting, at its +very foundation, young men who were to prove themselves the +leaders of the future. This experience may admit of being +repeated, if it be carefully borne in mind that young men of +promise are to be avoided and young men of performance only to be +considered. The performance need not be striking: ex pede Herculem +may be possible; but we must be sure of the soundness of our +judgment before accepting our Hercules. This requires a master. +Clerk-Maxwell, who never left his native island to visit our +shores, is entitled to honor as a promoter of American science for +seeing the lion's paw in the early efforts of Rowland, for which +the latter was unable to find a medium of publication in his own +country. It must also be admitted that the task is more serious +now than it was then, because, from the constantly increasing +specialization of science, it has become difficult for a +specialist in one line to ascertain the soundness of work in +another. With all the risks that may be involved in the +proceeding, it will be quite possible to select an effective body +of leaders, young and old, with whom an institution can begin. The +wants of these men will be of the most varied kind. One needs +scarcely more than a study and library; another must have small +pieces of apparatus which he can perhaps design and make for +himself. Another may need apparatus and appliances so expensive +that only an institution at least as wealthy as an ordinary +university would be able to supply them. The apparatus required by +others will be very largely human--assistants of every grade, from +university graduates of the highest standing down to routine +drudges and day-laborers. Workrooms there must be; but it is +hardly probable that buildings and laboratories of a highly +specialized character will be required at the outset. The best +counsel will be necessary at every step, and in this respect the +institution must start from simple beginnings and grow slowly. +Leaders must be added one by one, each being judged by those who +have preceded him before becoming in his turn a member of the +body. As the body grows its members must be kept in personal +touch, talk together, pull together, and act together. + +The writer submits these views to the great body of his fellow- +citizens interested in the promotion of American science with the +feeling that, though his conclusions may need amendment in +details, they rest upon facts of the past and present which have +not received the consideration which they merit. What he most +strongly urges is that the whole subject of the most efficient +method of promoting research upon a higher plane shall be +considered with special reference to conditions in our own +country; and that the lessons taught by the history and progress +of scientific research in all countries shall be fully weighed and +discussed by those most interested in making this form of effort a +more important feature of our national life. When this is done, he +will feel that his purpose in inviting special consideration to +his individual views has been in great measure reached. + + + + + +XII + +CAN WE MAKE IT RAIN? + + +To the uncritical observer the possible achievements of invention +and discovery seem boundless. Half a century ago no idea could +have appeared more visionary than that of holding communication in +a few seconds of time with our fellows in Australia, or having a +talk going on viva voce between a man in Washington and another in +Boston. The actual attainment of these results has naturally given +rise to the belief that the word "impossible" has disappeared from +our vocabulary. To every demonstration that a result cannot be +reached the answer is, Did not one Lardner, some sixty years ago, +demonstrate that a steamship could not cross the Atlantic? If we +say that for every actual discovery there are a thousand visionary +projects, we are told that, after all, any given project may be +the one out of the thousand. + +In a certain way these hopeful anticipations are justified. We +cannot set any limit either to the discovery of new laws of nature +or to the ingenious combination of devices to attain results which +now look impossible. The science of to-day suggests a boundless +field of possibilities. It demonstrates that the heat which the +sun radiates upon the earth in a single day would suffice to drive +all the steamships now on the ocean and run all the machinery on +the land for a thousand years. The only difficulty is how to +concentrate and utilize this wasted energy. From the stand-point +of exact science aerial navigation is a very simple matter. We +have only to find the proper combination of such elements as +weight, power, and mechanical force. Whenever Mr. Maxim can make +an engine strong and light enough, and sails large, strong, and +light enough, and devise the machinery required to connect the +sails and engine, he will fly. Science has nothing but encouraging +words for his project, so far as general principles are concerned. +Such being the case, I am not going to maintain that we can never +make it rain. + +But I do maintain two propositions. If we are ever going to make +it rain, or produce any other result hitherto unattainable, we +must employ adequate means. And if any proposed means or agency is +already familiar to science, we may be able to decide beforehand +whether it is adequate. Let us grant that out of a thousand +seemingly visionary projects one is really sound. Must we try the +entire thousand to find the one? By no means. The chances are that +nine hundred of them will involve no agency that is not already +fully understood, and may, therefore, be set aside without even +being tried. To this class belongs the project of producing rain +by sound. As I write, the daily journals are announcing the +brilliant success of experiments in this direction; yet I +unhesitatingly maintain that sound cannot make rain, and propose +to adduce all necessary proof of my thesis. The nature of sound is +fully understood, and so are the conditions under which the +aqueous vapor in the atmosphere may be condensed. Let us see how +the case stands. + +A room of average size, at ordinary temperature and under usual +conditions, contains about a quart of water in the form of +invisible vapor. The whole atmosphere is impregnated with vapor in +about the same proportion. We must, however, distinguish between +this invisible vapor and the clouds or other visible masses to +which the same term is often applied. The distinction may be very +clearly seen by watching the steam coming from the spout of a +boiling kettle. Immediately at the spout the escaping steam is +transparent and invisible; an inch or two away a white cloud is +formed, which we commonly call steam, and which is seen belching +out to a distance of one or more feet, and perhaps filling a +considerable space around the kettle; at a still greater distance +this cloud gradually disappears. Properly speaking, the visible +cloud is not vapor or steam at all, but minute particles or drops +of water in a liquid state. The transparent vapor at the mouth of +the kettle is the true vapor of water, which is condensed into +liquid drops by cooling; but after being diffused through the air +these drops evaporate and again become true vapor. Clouds, then, +are not formed of true vapor, but consist of impalpable particles +of liquid water floating or suspended in the air. + +But we all know that clouds do not always fall as rain. In order +that rain may fall the impalpable particles of water which form +the cloud must collect into sensible drops large enough to fall to +the earth. Two steps are therefore necessary to the formation of +rain: the transparent aqueous vapor in the air must be condensed +into clouds, and the material of the clouds must agglomerate into +raindrops. + +No physical fact is better established than that, under the +conditions which prevail in the atmosphere, the aqueous vapor of +the air cannot be condensed into clouds except by cooling. It is +true that in our laboratories it can be condensed by compression. +But, for reasons which I need not explain, condensation by +compression cannot take place in the air. The cooling which +results in the formation of clouds and rain may come in two ways. +Rains which last for several hours or days are generally produced +by the intermixture of currents of air of different temperatures. +A current of cold air meeting a current of warm, moist air in its +course may condense a considerable portion of the moisture into +clouds and rain, and this condensation will go on as long as the +currents continue to meet. In a hot spring day a mass of air which +has been warmed by the sun, and moistened by evaporation near the +surface of the earth, may rise up and cool by expansion to near +the freezing-point. The resulting condensation of the moisture may +then produce a shower or thunder-squall. But the formation of +clouds in a clear sky without motion of the air or change in the +temperature of the vapor is simply impossible. We know by abundant +experiments that a mass of true aqueous vapor will never condense +into clouds or drops so long as its temperature and the pressure +of the air upon it remain unchanged. + +Now let us consider sound as an agent for changing the state of +things in the air. It is one of the commonest and simplest +agencies in the world, which we can experiment upon without +difficulty. It is purely mechanical in its action. When a bomb +explodes, a certain quantity of gas, say five or six cubic yards, +is suddenly produced. It pushes aside and compresses the +surrounding air in all directions, and this motion and compression +are transmitted from one portion of the air to another. The amount +of motion diminishes as the square of the distance; a simple +calculation shows that at a quarter of a mile from the point of +explosion it would not be one ten-thousandth of an inch. The +condensation is only momentary; it may last the hundredth or the +thousandth of a second, according to the suddenness and violence +of the explosion; then elasticity restores the air to its original +condition and everything is just as it was before the explosion. A +thousand detonations can produce no more effect upon the air, or +upon the watery vapor in it, than a thousand rebounds of a small +boy's rubber ball would produce upon a stonewall. So far as the +compression of the air could produce even a momentary effect, it +would be to prevent rather than to cause condensation of its +vapor, because it is productive of heat, which produces +evaporation, not condensation. + +The popular notion that sound may produce rain is founded +principally upon the supposed fact that great battles have been +followed by heavy rains. This notion, I believe, is not confirmed +by statistics; but, whether it is or not, we can say with +confidence that it was not the sound of the cannon that produced +the rain. That sound as a physical factor is quite insignificant +would be evident were it not for our fallacious way of measuring +it. The human ear is an instrument of wonderful delicacy, and when +its tympanum is agitated by a sound we call it a "concussion" +when, in fact, all that takes place is a sudden motion back and +forth of a tenth, a hundredth, or a thousandth of an inch, +accompanied by a slight momentary condensation. After these +motions are completed the air is exactly in the same condition as +it was before; it is neither hotter nor colder; no current has +been produced, no moisture added. + +If the reader is not satisfied with this explanation, he can try a +very simple experiment which ought to be conclusive. If he will +explode a grain of dynamite, the concussion within a foot of the +point of explosion will be greater than that which can be produced +by the most powerful bomb at a distance of a quarter of a mile. In +fact, if the latter can condense vapor a quarter of a mile away, +then anybody can condense vapor in a room by slapping his hands. +Let us, therefore, go to work slapping our hands, and see how long +we must continue before a cloud begins to form. + +What we have just said applies principally to the condensation of +invisible vapor. It may be asked whether, if clouds are already +formed, something may not be done to accelerate their condensation +into raindrops large enough to fall to the ground. This also may +be the subject of experiment. Let us stand in the steam escaping +from a kettle and slap our hands. We shall see whether the steam +condenses into drops. I am sure the experiment will be a failure; +and no other conclusion is possible than that the production of +rain by sound or explosions is out of the question. + +It must, however, be added that the laws under which the +impalpable particles of water in clouds agglomerate into drops of +rain are not yet understood, and that opinions differ on this +subject. Experiments to decide the question are needed, and it is +to be hoped that the Weather Bureau will undertake them. For +anything we know to the contrary, the agglomeration may be +facilitated by smoke in the air. If it be really true that rains +have been produced by great battles, we may say with confidence +that they were produced by the smoke from the burning powder +rising into the clouds and forming nuclei for the agglomeration +into drops, and not by the mere explosion. If this be the case, if +it was the smoke and not the sound that brought the rain, then by +burning gunpowder and dynamite we are acting much like Charles +Lamb's Chinamen who practised the burning of their houses for +several centuries before finding out that there was any cheaper +way of securing the coveted delicacy of roast pig. + +But how, it may be asked, shall we deal with the fact that Mr. +Dyrenforth's recent explosions of bombs under a clear sky in Texas +were followed in a few hours, or a day or two, by rains in a +region where rain was almost unknown? I know too little about the +fact, if such it be, to do more than ask questions about it +suggested by well-known scientific truths. If there is any +scientific result which we can accept with confidence, it is that +ten seconds after the sound of the last bomb died away, silence +resumed her sway. From that moment everything in the air-- +humidity, temperature, pressure, and motion--was exactly the same +as if no bomb had been fired. Now, what went on during the hours +that elapsed between the sound of the last bomb and the falling of +the first drop of rain? Did the aqueous vapor already in the +surrounding air slowly condense into clouds and raindrops in +defiance of physical laws? If not, the hours must have been +occupied by the passage of a mass of thousands of cubic miles of +warm, moist air coming from some other region to which the sound +could not have extended. Or was Jupiter Pluvius awakened by the +sound after two thousand years of slumber, and did the laws of +nature become silent at his command? When we transcend what is +scientifically possible, all suppositions are admissible; and we +leave the reader to take his choice between these and any others +he may choose to invent. + +One word in justification of the confidence with which I have +cited established physical laws. It is very generally supposed +that most great advances in applied science are made by rejecting +or disproving the results reached by one's predecessors. Nothing +could be farther from the truth. As Huxley has truly said, the +army of science has never retreated from a position once gained. +Men like Ohm and Maxwell have reduced electricity to a +mathematical science, and it is by accepting, mastering, and +applying the laws of electric currents which they discovered and +expounded that the electric light, electric railway, and all other +applications of electricity have been developed. It is by applying +and utilizing the laws of heat, force, and vapor laid down by such +men as Carnot and Regnault that we now cross the Atlantic in six +days. These same laws govern the condensation of vapor in the +atmosphere; and I say with confidence that if we ever do learn to +make it rain, it will be by accepting and applying them, and not +by ignoring or trying to repeal them. + +How much the indisposition of our government to secure expert +scientific evidence may cost it is strikingly shown by a recent +example. It expended several million dollars on a tunnel and +water-works for the city of Washington, and then abandoned the +whole work. Had the project been submitted to a commission of +geologists, the fact that the rock-bed under the District of +Columbia would not stand the continued action of water would have +been immediately reported, and all the money expended would have +been saved. The fact is that there is very little to excite +popular interest in the advance of exact science. Investigators +are generally quiet, unimpressive men, rather diffident, and +wholly wanting in the art of interesting the public in their work. +It is safe to say that neither Lavoisier, Galvani, Ohm, Regnault, +nor Maxwell could have gotten the smallest appropriation through +Congress to help make discoveries which are now the pride of our +century. They all dealt in facts and conclusions quite devoid of +that grandeur which renders so captivating the project of +attacking the rains in their aerial stronghold with dynamite +bombs. + + + + + +XIII + +THE ASTRONOMICAL EPHEMERIS AND THE NAUTICAL ALMANAC + +[Footnote: Read before the U S Naval Institute, January 10, 1879.] + + +Although the Nautical Almanacs of the world, at the present time, +are of comparatively recent origin, they have grown from small +beginnings, the tracing of which is not unlike that of the origin +of species by the naturalist of the present day. Notwithstanding +its familiar name, it has always been designed rather for +astronomical than for nautical purposes. Such a publication would +have been of no use to the navigator before he had instruments +with which to measure the altitudes of the heavenly bodies. The +earlier navigators seldom ventured out of sight of land, and +during the night they are said to have steered by the "Cynosure" +or constellation of the Great Bear, a practice which has brought +the name of the constellation into our language of the present day +to designate an object on which all eyes are intently fixed. This +constellation was a little nearer the pole in former ages than at +the present time; still its distance was always so great that its +use as a mark of the northern point of the horizon does not +inspire us with great respect for the accuracy with which the +ancient navigators sought to shape their course. + +The Nautical Almanac of the present day had its origin in the +Astronomical Ephemerides called forth by the needs of predictions +of celestial motions both on the part of the astronomer and the +citizen. So long as astrology had a firm hold on the minds of men, +the positions of the planets were looked to with great interest. +The theories of Ptolemy, although founded on a radically false +system, nevertheless sufficed to predict the position of the sun, +moon, and planets, with all the accuracy necessary for the +purposes of the daily life of the ancients or the sentences of +their astrologers. Indeed, if his tables were carried down to the +present time, the positions of the heavenly bodies would be so few +degrees in error that their recognition would be very easy. The +times of most of the eclipses would be predicted within a few +hours, and the conjunctions of the planets within a few days. Thus +it was possible for the astronomers of the Middle Ages to prepare +for their own use, and that of the people, certain rude +predictions respecting the courses of the sun and moon and the +aspect of the heavens, which served the purpose of daily life and +perhaps lessened the confusion arising from their complicated +calendars. In the signs of the zodiac and the different effects +which follow from the sun and moon passing from sign to sign, +still found in our farmers' almanacs, we have the dying traces of +these ancient ephemerides. + +The great Kepler was obliged to print an astrological almanac in +virtue of his position as astronomer of the court of the King of +Austria. But, notwithstanding the popular belief that astronomy +had its origin in astrology, the astronomical writings of all ages +seem to show that the astronomers proper never had any belief in +astrology. To Kepler himself the necessity for preparing this +almanac was a humiliation to which he submitted only through the +pressure of poverty. Subsequent ephemerides were prepared with +more practical objects. They gave the longitudes of the planets, +the position of the sun, the time of rising and setting, the +prediction of eclipses, etc. + +They have, of course, gradually increased in accuracy as the +tables of the celestial motions were improved from time to time. +At first they were not regular, annual publications, issued by +governments, as at the present time, but the works of individual +astronomers who issued their ephemerides for several years in +advance, at irregular intervals. One man might issue one, two, or +half a dozen such volumes, as a private work, for the benefit of +his fellows, and each might cover as many years as he thought +proper. + +The first publication of this sort, which I have in my possession, +is the Ephemerides of Manfredi, of Bonn, computed for the years +1715 to 1725, in two volumes. + +Of the regular annual ephemerides the earliest, so far as I am +aware, is the Connaissance des Temps or French Nautical Almanac. +The first issue was in the year 1679, by Picard, and it has been +continued without interruption to the present time. Its early +numbers were, of course, very small, and meagre in their details. +They were issued by the astronomers of the French Academy of +Sciences, under the combined auspices of the academy and the +government. They included not merely predictions from the tables, +but also astronomical observations made at the Paris Observatory +or elsewhere. When the Bureau of Longitudes was created in 1795, +the preparation of the work was intrusted to it, and has remained +in its charge until the present time. As it is the oldest, so, in +respect at least to number of pages, it is the largest ephemeris +of the present time. The astronomical portion of the volume for +1879 fills more than seven hundred pages, while the table of +geographical positions, which has always been a feature of the +work, contains nearly one hundred pages more. + +The first issue of the British Nautical Almanac was that for the +year 1767 and appeared in 1766. It differs from the French Almanac +in owing its origin entirely to the needs of navigation. The +British nation, as the leading maritime power of the world, was +naturally interested in the discovery of a method by which the +longitude could be found at sea. As most of my hearers are +probably aware, there was, for many years, a standing offer by the +British government, of ten thousand pounds for the discovery of a +practical and sufficiently accurate method of attaining this +object. If I am rightly informed, the requirement was that a ship +should be able to determine the Greenwich time within two minutes, +after being six months at sea. When the office of Astronomer Royal +was established in 1765, the duty of the incumbent was declared to +be "to apply himself with the most exact care and diligence to the +rectifying the Tables of the Motions of the Heavens, and the +places of the Fixed Stars in order to find out the so much desired +Longitude at Sea for the perfecting the Art of Navigation." + +About the middle of the last century the lunar tables were so far +improved that Dr. Maskelyne considered them available for +attaining this long-wished-for object. The method which I think +was then, for the first time, proposed was the now familiar one of +lunar distances. Several trials of the method were made by +accomplished gentlemen who considered that nothing was wanting to +make it practical at sea but a Nautical Ephemeris. The tables of +the moon, necessary for the purpose, were prepared by Tobias +Mayer, of Gottingen, and the regular annual issue of the work was +commenced in 1766, as already stated. Of the reward which had been +offered, three thousand pounds were paid to the widow of Mayer, +and three thousand pounds to the celebrated mathematician Euler +for having invented the methods used by Mayer in the construction +of his tables. The issue of the Nautical Ephemeris was intrusted +to Dr. Maskelyne. Like other publications of this sort this +ephemeris has gradually increased in volume. During the first +sixty or seventy years the data were extremely meagre, including +only such as were considered necessary for the determination of +positions. + +In 1830 the subject of improving the Nautical Almanac was referred +by the Lord Commissioners of the Admiralty to a committee of the +Astronomical Society of London. A subcommittee, including eleven +of the most distinguished astronomers and one scientific +navigator, made an, exhaustive report, recommending a radical +rearrangement and improvement of the work. The recommendations of +this committee were first carried into effect in the Nautical +Almanac for the year 1834. The arrangement of the Navigator's +Ephemeris then devised has been continued in the British Almanac +to the present time. + +A good deal of matter has been added to the British Almanac during +the forty years and upwards which have elapsed, but it has been +worked in rather by using smaller type and closer printing than by +increasing the number of pages. The almanac for 1834 contains five +hundred and seventeen pages and that for 1880 five hundred and +nineteen pages. The general aspect of the page is now somewhat +crowded, yet, considering the quantity of figures on each page the +arrangement is marvellously clear and legible. + +The Spanish "Almanaque Nautico" has been issued since the +beginning of the century. Like its fellows it has been gradually +enlarged and improved, in recent times, and is now of about the +same number of pages with the British and American almanacs. As a +rule there is less matter on a page, so that the data actually +given are not so complete as in some other publications. + +In Germany two distinct publications of this class are issued, the +one purely astronomical, the other purely nautical. + +The astronomical publication has been issued for more than a +century under the title of "Berliner Astronomisches Jahrbuch." It +is intended principally for the theoretical astronomer, and in +respect to matter necessary to the determinations of positions on +the earth it is rather meagre. It is issued by the Berlin +Observatory, at the expense of the government. + +The companion of this work, intended for the use of the German +marine, is the "Nautisches Jahrbuch," prepared and issued under +the direction of the minister of commerce and public works. It is +copied largely from the British Nautical Almanac, and in respect +to arrangement and data is similar to our American Nautical +Almanac, prepared for the use of navigators, giving, however, more +matter, but in a less convenient form. The right ascension and +declination of the moon are given for every three hours instead of +for every hour; one page of each month is devoted to eclipses of +Jupiter's satellites, phenomena which we never consider necessary +in the nautical portion of our own almanac. At the end of the work +the apparent positions of seventy or eighty of the brightest stars +are given for every ten days, while it is considered that our own +navigators will be satisfied with the mean places for the +beginning of the year. At the end is a collection of tables which +I doubt whether any other than a German navigator would ever use. +Whether they use them or not I am not prepared to say. + +The preceding are the principal astronomical and nautical +ephemerides of the world, but there are a number of minor +publications, of the same class, of which I cannot pretend to give +a complete list. Among them is the Portuguese Astronomical +Ephemeris for the meridian of the University of Coimbra, prepared +for Portuguese navigators. I do not know whether the Portuguese +navigators really reckon their longitudes from this point: if they +do the practice must be attended with more or less confusion. All +the matter is given by months, as in the solar and lunar ephemeris +of our own and the British Almanac. For the sun we have its +longitude, right ascension, and declination, all expressed in arc +and not in time. The equation of time and the sidereal time of +mean noon complete the ephemeris proper. The positions of the +principal planets are given in no case oftener than for every +third day. The longitude and latitude of the moon are given for +noon and midnight. One feature not found in any other almanac is +the time at which the moon enters each of the signs of the zodiac. +It may be supposed that this information is designed rather for +the benefit of the Portuguese landsman than of the navigator. The +right ascensions and declinations of the moon and the lunar +distances are also given for intervals of twelve hours. Only the +last page gives the eclipses of the satellites of Jupiter. The +Fixed Stars are wholly omitted. + +An old ephemeris, and one well known in astronomy is that +published by the Observatory of Milan, Italy, which has lately +entered upon the second century of its existence. Its data are +extremely meagre and of no interest whatever to the navigator. The +greater part of the volume is taken up with observations at the +Milan Observatory. + +Since taking charge of the American Ephemeris I have endeavored to +ascertain what nautical almanacs are actually used by the +principal maritime nations of Europe. I have been able to obtain +none except those above mentioned. As a general rule I think the +British Nautical Almanac is used by all the northern nations, as +already indicated. The German Nautical Jahrbuch is principally a +reprint from the British. The Swedish navigators, being all well +acquainted with the English language, use the British Almanac +without change. The Russian government, however, prints an +explanation of the various terms in the language of their own +people and binds it in at the end of the British Almanac. This +explanation includes translations of the principal terms used in +the heading of pages, such as the names of the months and days, +the different planets, constellations, and fixed stars, and the +phenomena of angle and time. They have even an index of their own +in which the titles of the different articles are given in +Russian. This explanation occupies, in all, seventy-five pages-- +more than double that taken up by the original explanation. + +One of the first considerations which strikes us in comparing +these multitudinous publications is the confusion which must arise +from the use of so many meridians. If each of these southern +nations, the Spanish and Portuguese for instance, actually use a +meridian of their own, the practice must lead to great confusion. +If their navigators do not do so but refer their longitudes to the +meridian of Greenwich, then their almanacs must be as good as +useless. They would find it far better to buy an ephemeris +referred to the meridian of Greenwich than to attempt to use their +own The northern nations, I think, have all begun to refer to the +meridian of Greenwich, and the same thing is happily true of our +own marine. We may, therefore, hope that all commercial nations +will, before long, refer their longitudes to one and the same +meridian, and the resulting confusion be thus avoided. + +The preparation of the American Ephemeris and Nautical Almanac was +commenced in 1849, under the superintendence of the late Rear- +Admiral, then Lieutenant, Charles Henry Davis. The first volume to +be issued was that for the year 1855. Both in the preparation of +that work and in the connected work of mapping the country, the +question of the meridian to be adopted was one of the first +importance, and received great attention from Admiral Davis, who +made an able report on the subject. Our situation was in some +respects peculiar, owing to the great distance which separated us +from Europe and the uncertainty of the exact difference of +longitude between the two continents. It was hardly practicable to +refer longitudes in our own country to any European meridian. The +attempt to do so would involve continual changes as the +transatlantic longitude was from time to time corrected. On the +other hand, in order to avoid confusion in navigation, it was +essential that our navigators should continue to reckon from the +meridian of Greenwich. The trouble arising from uncertainty of the +exact longitude does not affect the navigator, because, for his +purpose, astronomical precision is not necessary. + +The wisest solution was probably that embodied in the act of +Congress, approved September 28, 1850, on the recommendation of +Lieutenant Davis, if I mistake not. "The meridian of the +Observatory at Washington shall be adopted and used as the +American meridian for all astronomical purposes, and the meridian +of Greenwich shall be adopted for all nautical purposes." The +execution of this law necessarily involves the question, "What +shall be considered astronomical and what nautical purposes?" +Whether it was from the difficulty of deciding this question, or +from nobody's remembering the law, the latter has been practically +a dead letter. Surely, if there is any region of the globe which +the law intended should be referred to the meridian of Washington, +it is the interior of our own country. Yet, notwithstanding the +law, all acts of Congress relating to the territories have, so far +as I know, referred everything to the meridian of Greenwich and +not to that of Washington. Even the maps issued by our various +surveys are referred to the same transatlantic meridian. The +absurdity culminated in a local map of the city of Washington and +the District of Columbia, issued by private parties, in 1861, in +which we find even the meridians passing through the city of +Washington referred to a supposed Greenwich. + +This practice has led to a confusion which may not be evident at +first sight, but which is so great and permanent that it may be +worth explaining. If, indeed, we could actually refer all our +longitudes to an accurate meridian of Greenwich in the first +place; if, for instance, any western region could be at once +connected by telegraph with the Greenwich Observatory, and thus +exchange longitude signals night after night, no trouble or +confusion would arise from referring to the meridian of Greenwich. +But this, practically, cannot be done. All our interior longitudes +have been and are determined differentially by comparison with +some point in this country. One of the most frequent points of +reference used this way has been the Cambridge Observatory. +Suppose, then, a surveyor at Omaha makes a telegraphic longitude +determination between that point and the Cambridge Observatory. +Since he wants his longitude reduced to Greenwich, he finds some +supposed longitude of the Cambridge Observatory from Greenwich and +adds that to his own longitude. Thus, what he gives is a longitude +actually determined, plus an assumed longitude of Cambridge, and, +unless the assumed longitude of Cambridge is distinctly marked on +his maps, we may not know what it is, + +After a while a second party determines the longitude of Ogden +from Cambridge. In the mean time, the longitude of Cambridge from +Greenwich has been corrected, and we have a longitude of Ogden +which will be discordant with that of Omaha, owing to the change +in the longitude of Cambridge. A third party determines the +longitudes of, let us suppose, St. Louis from Washington, he adds +the assumed longitudes of Washington from Greenwich which may not +agree with either of the longitudes of Cambridge and gets his +longitude. Thus we have a series of results for our western +longitude all nominally referred to the meridian of Greenwich, but +actually referred to a confused collection of meridians, nobody +knows what. If the law had only provided that the longitude of +Washington from Greenwich should be invariably fixed at a certain +quantity, say 77 degrees 3', this confusion would not have arisen. +It is true that the longitude thus established by law might not +have been perfectly correct, but this would not cause any trouble +nor confusion. Our longitude would have been simply referred to a +certain assumed Greenwich, the small error of which would have +been of no importance to the navigator or astronomer. It would +have differed from the present system only in that the assumed +Greenwich would have been invariable instead of dancing about from +time to time as it has done under the present system. You +understand that when the astronomer, in computing an interior +longitude, supposes that of Cambridge from Greenwich to be a +certain definite amount, say 4h 44m 30s, what he actually does is +to count from a meridian just that far east of Cambridge. When he +changes the assumed longitude of Cambridge he counts from a +meridian farther east or farther west of his former one: in other +words, he always counts from an assumed Greenwich, which changes +its position from time to time, relative to our own country. + +Having two meridians to look after, the form of the American +Ephemeris, to be best adapted to the wants both of navigators and +astronomers was necessarily peculiar. Had our navigators referred +their longitudes to any meridian of our own country the +arrangement of the work need not have differed materially from +that of foreign ones. But being referred to a meridian far outside +our limits and at the same time designed for use within those +limits, it was necessary to make a division of the matter. +Accordingly, the American Ephemeris has always been divided into +two parts: the first for the use of navigators, referred to the +meridian of Greenwich, the second for that of astronomers, +referred to the meridian of Washington. The division of the matter +without serious duplication is more easy than might at first be +imagined. In explaining it, I will take the ephemeris as it now +is, with the small changes which have been made from time to time. + +One of the purposes of any ephemeris, and especially of that of +the navigators, is to give the position of the heavenly bodies at +equidistant intervals of time, usually one day. Since it is noon +at some point of the earth all the time, it follows that such an +ephemeris will always be referred to noon at some meridian. What +meridian this shall be is purely a practical question, to be +determined by convenience and custom. Greenwich noon, being that +necessarily used by the navigator, is adopted as the standard, but +we must not conclude that the ephemeris for Greenwich noon is +referred to the meridian of Greenwich in the sense that we refer a +longitude to that meridian. Greenwich noon is 18h 51m 48s, +Washington mean time; so the ephemeris which gives data for every +Greenwich noon may be considered as referred to the meridian of +Washington giving the data for 17h 51m 48s, Washington time, every +day. The rule adopted, therefore, is to have all the ephemerides +which refer to absolute time, without any reference to a meridian, +given for Greenwich noon, unless there may be some special reason +to the contrary. For the needs of the navigator and the +theoretical astronomer these are the most convenient epochs. + +Another part of the ephemeris gives the position of the heavenly +bodies, not at equidistant intervals, but at transit over some +meridian. For this purpose the meridian of Washington is chosen +for obvious reasons. The astronomical part of our ephemeris, +therefore, gives the positions of the principal fixed stars, the +sun, moon, and all the larger planets at the moment of transit +over our own meridian. + +The third class of data in the ephemeris comprises phenomena to be +predicted and observed. Such are eclipses of the sun and moon, +occultations of fixed stars by the moon, and eclipses of Jupiter's +satellites. These phenomena are all given in Washington mean time +as being most convenient for observers in our own country. There +is a partial exception, however, in the case of eclipses of the +sun and moon. The former are rather for the world in general than +for our own country, and it was found difficult to arrange them to +be referred to the meridian of Washington without having the maps +referred to the same meridian. Since, however, the meridian of +Greenwich is most convenient outside of our own territory, and +since but a small portion of the eclipses are visible within it, +it is much the best to have the eclipses referred entirely to the +meridian of Greenwich. I am the more ready to adopt this change +because when the eclipses are to be computed for our own country +the change of meridians will be very readily understood by those +who make the computation. + +It may be interesting to say something of the tables and theories +from which the astronomical ephemerides are computed. To +understand them completely it is necessary to trace them to their +origin. The problem of calculating the motions of the heavenly +bodies and the changes in the aspect of the celestial sphere was +one of the first with which the students of astronomy were +occupied. Indeed, in ancient times, the only astronomical problems +which could be attacked were of this class, for the simple reason +that without the telescope and other instruments of research it +was impossible to form any idea of the physical constitution of +the heavenly bodies. To the ancients the stars and planets were +simply points or surfaces in motion. They might have guessed that +they were globes like that on which we live, but they were unable +to form any theory of the nature of these globes. Thus, in The +Almagest of Ptolemy, the most complete treatise on the ancient +astronomy which we possess, we find the motions of all the +heavenly bodies carefully investigated and tables given for the +convenient computation of their positions. Crude and imperfect +though these tables may be, they were the beginnings from which +those now in use have arisen. + +No radical change was made in the general principles on which +these theories and tables were constructed until the true system +of the world was propounded by Copernicus. On this system the +apparent motion of each planet in the epicycle was represented by +a motion of the earth around the sun, and the problem of +correcting the position of the planet on account of the epicycle +was reduced to finding its geocentric from its heliocentric +position. This was the greatest step ever taken in theoretical +astronomy, yet it was but a single step. So far as the materials +were concerned and the mode of representing the planetary motions, +no other radical advance was made by Copernicus. Indeed, it is +remarkable that he introduced an epicycle which was not considered +necessary by Ptolemy in order to represent the inequalities in the +motions of the planets around the sun. + +The next great advance made in the theory of the planetary motion +was the discovery by Kepler of the celebrated laws which bear his +name. When it was established that each planet moved in an ellipse +having the sun in one focus it became possible to form tables of +the motions of the heavenly bodies much more accurate than had +before been known. Such tables were published by Kepler in 1632, +under the name of Rudolphine Tables, in memory of his patron, the +Emperor Rudolph. But the laws of Kepler took no account of the +action of the planets on one another. It is well known that if +each planet moved only under the influence of the gravitating +force of the sun its motion would accord rigorously with the laws +of Kepler, and the problems of theoretical astronomy would be +greatly simplified. When, therefore, the results of Kepler's laws +were compared with ancient and modern observations it was found +that they were not exactly represented by the theory. It was +evident that the elliptic orbits of the planets were subject to +change, but it was entirely beyond the power of investigation, at +that time, to assign any cause for such changes. Notwithstanding +the simplicity of the causes which we now know to produce them, +they are in form extremely complex. Without the knowledge of the +theory of gravitation it would be entirely out of the question to +form any tables of the planetary motions which would at all satisfy +our modern astronomers. + +When the theory of universal gravitation was propounded by Newton +he showed that a planet subjected only to the gravitation of a +central body, like the sun, would move in exact accordance with +Kepler's laws. But by his theory the planets must attract one +another and these attractions must cause the motions of each to +deviate slightly from the laws in question. Since such deviations +were actually observed it was very natural to conclude that they +were due to this cause, but how shall we prove it? To do this with +all the rigor required in a mathematical investigation it is +necessary to calculate the effect of the mutual action of the +planets in changing their orbits. This calculation must be made +with such precision that there shall be no doubt respecting the +results of the theory. Then its results must be compared with the +best observations. If the slightest outstanding difference is +established there is something wrong and the requirements of +astronomical science are not satisfied. The complete solution of +this problem was entirely beyond the power of Newton. When his +methods of research were used he was indeed able to show that the +mutual action of the planets would produce deviations in their +motions of the same general nature with those observed, but he was +not able to calculate these deviations with numerical exactness. +His most successful attempt in this direction was perhaps made in +the case of the moon. He showed that the sun's disturbing force on +this body would produce several inequalities the existence of +which had been established by observation, and he was also able to +give a rough estimate of their amount, but this was as far as his +method could go. A great improvement had to be made, and this was +effected not by English, but by continental mathematicians. + +The latter saw, clearly, that it was impossible to effect the +required solution by the geometrical mode of reasoning employed by +Newton. The problem, as it presented itself to their minds, was to +find algebraic expressions for the positions of the planets at any +time. The latitude, longitude, and radius-vector of each planet +are constantly varying, but they each have a determined value at +each moment of time. They may therefore be regarded as functions +of the time, and the problem was to express these functions by +algebraic formulae. These algebraic expressions would contain, +besides the time, the elements of the planetary orbits to be +derived from observation. The time which we may suppose to be +represented algebraically by the symbol t, would remain as an +unknown quantity to the end. What the mathematician sought to do +was to present the astronomer with a series of algebraic +expressions containing t as an indeterminate quantity, and so, by +simply substituting for t any year and fraction of a year +whatever--1600, 1700, 1800, for example, the result would give the +latitude, longitude, or radius-vector of a planet. + +The problem as thus presented was one of the most difficult we can +perceive of, but the difficulty was only an incentive to attacking +it with all the greater energy. So long as the motion was supposed +purely elliptical, so long as the action of the planets was +neglected, the problem was a simple one, requiring for its +solution only the analytic geometry of the ellipse. The real +difficulties commenced when the mutual action of the planets was +taken into account. It is, of course, out of the question to give +any technical description or analysis of the processes which have +been invented for solving the problem; but a brief historical +sketch may not be out of place. A complete and rigorous solution +of the problem is out of the question--that is, it is impossible +by any known method to form an algebraic expression for the co- +ordinates of a planet which shall be absolutely exact in a +mathematical sense. In whatever way we go to work the expression +comes out in the form of an infinite series of terms, each term +being, on the whole, a little smaller as we increase the number. +So, by increasing the number of these various terms, we can +approach nearer and nearer to a mathematical exactness, but can +never reach it. The mathematician and astronomer have to be +satisfied when they have carried the solution so far that the +neglected quantities are entirely beyond the powers of +observation. + +Mathematicians have worked upon the problem in its various phases +for nearly two centuries, and many improvements in detail have, +from time to time, been made, but no general method, applicable to +all cases, has been devised. One plan is to be used in treating +the motion of the moon, another for the interior planets, another +for Jupiter and Saturn, another for the minor planets, and so on. +Under these circumstances it will not surprise you to learn that +our tables of the celestial motions do not, in general, correspond +in accuracy to the present state of practical astronomy. There is +no authority and no office in the world whose duty it is to look +after the preparations of the formulae I have described. The work +of computing them has been almost entirely left to individual +mathematicians whose taste lay in that direction, and who have +sometimes devoted the greater part of their lives to calculations +on a single part of the work. As a striking instance of this, the +last great work on the Motion of the Moon, that of Delaunay, of +Paris, involved some fifteen years of continuous hard labor. + +Hansen, of Germany, who died five years ago, devoted almost his +whole life to investigations of this class and to the development +of new methods of computation. His tables of the moon are those +now used for predicting the places of the moon in all the +ephemerides of the world. + +The only successful attempt to prepare systematic tables for all +the large planets is that completed by Le Verrier just before his +death; but he used only a small fraction of the material at his +disposal, and did not employ the modern methods, confining himself +wholly to those invented by his countrymen about the beginning of +the present century. For him Jacobi and Hansen had lived in vain. + +The great difficulty which besets the subject arises from the fact +that mathematical processes alone will not give us the position of +a planet, there being seven unknown quantities for each planet +which must be determined by observations. A planet, for instance, +may move in any ellipse whatever, having the sun in one focus, and +it is impossible to tell what ellipse it is, except from +observation. The mean motion of a planet, or its period of +revolution, can only be determined by a long series of +observations, greater accuracy being obtained the longer the +observations are continued. Before the time of Bradley, who +commenced work at the Greenwich Observatory about 1750, the +observations were so far from accurate that they are now of no use +whatever, unless in exceptional cases. Even Bradley's observations +are in many cases far less accurate than those made now. In +consequence, we have not heretofore had a sufficiently extended +series of observations to form an entirely satisfactory theory of +the celestial motions. + +As a consequence of the several difficulties and drawbacks, when +the computation of our ephemeris was started, in the year 1849, +there were no tables which could be regarded as really +satisfactory in use. In the British Nautical Almanac the places of +the moon were derived from the tables of Burckhardt published in +the year 1812. You will understand, in a case like this, no +observations subsequent to the issue of the tables are made use +of; the place of the moon of any day, hour, and minute of +Greenwich time, mean time, was precisely what Burckhardt would +have computed nearly a half a century before. Of the tables of the +larger planets the latest were those of Bouvard, published in +1812, while the places of Venus were from tables published by +Lindenau in 1810. Of course such tables did not possess +astronomical accuracy. At that time, in the case of the moon, +completely new tables were constructed from the results reached by +Professor Airy in his reduction of the Greenwich observations of +the moon from 1750 to 1830. These were constructed under the +direction of Professor Pierce and represented the places of the +moon with far greater accuracy than the older tables of +Burckhardt. For the larger planets corrections were applied to the +older tables to make them more nearly represent observations +before new ones were constructed. These corrections, however, have +not proved satisfactory, not being founded on sufficiently +thorough investigations. Indeed, the operation of correcting +tables by observation, as we would correct the dead-reckoning of a +ship, is a makeshift, the result of which must always be somewhat +uncertain, and it tends to destroy that unity which is an +essential element of the astronomical ephemeris designed for +permanent future use. The result of introducing them, while no +doubt an improvement on the old tables, has not been all that +should be desired. The general lack of unity in the tables +hitherto employed is such that I can only state what has been done +by mentioning each planet in detail. + +For Mercury, new tables were constructed by Professor Winlock, +from formulae published by Le Verrier in 1846. These tables have, +however, been deviating from the true motion of the planet, owing +to the motion of the perihelion of Mercury, subsequently +discovered by Le Verrier himself. They are now much less accurate +than the newer tables published by Le Verrier ten years later. + +Of Venus new tables were constructed by Mr. Hill in 1872. They are +more accurate than any others, being founded on later data than +those of Le Verrier, and are therefore satisfactory so far as +accuracy of prediction is concerned. + +The place of Mars, Jupiter, and Saturn are still computed from the +old tables, with certain necessary corrections to make them better +represent observations. + +The places of Uranus and Neptune are derived from new tables which +will probably be sufficiently accurate for some time to come. + +For the moon, Pierce's tables have been employed up to the year +1882 inclusive. Commencing with the ephemeris for the year 1883, +Hansen's tables are introduced with corrections to the mean +longitude founded on two centuries of observation. + +With so great a lack of uniformity, and in the absence of any +existing tables which have any other element of unity than that of +being the work of the same authors, it is extremely desirable that +we should be able to compute astronomical ephemerides from a +single uniform and consistent set of astronomical data. I hope, in +the course of years, to render this possible. + +When our ephemeris was first commenced, the corrections applied to +existing tables rendered it more accurate than any other. Since +that time, the introduction into foreign ephemerides of the +improved tables of Le Verrier have rendered them, on the whole, +rather more accurate than our own. In one direction, however, our +ephemeris will hereafter be far ahead of all others. I mean in its +positions of the fixed stars. This portion of it is of particular +importance to us, owing to the extent to which our government is +engaged in the determination of positions on this continent, and +especially in our western territories. Although the places of the +stars are determined far more easily than those of the planets, +the discussion of star positions has been in almost as backward a +state as planetary positions. The errors of old observers have +crept in and been continued through two generations of +astronomers. A systematic attempt has been made to correct the +places of the stars for all systematic errors of this kind, and +the work of preparing a catalogue of stars which shall be +completely adapted to the determination of time and longitude, +both in the fixed observatory and in the field, is now approaching +completion. The catalogue cannot be sufficiently complete to give +places of the stars for determining the latitude by the zenith +telescope, because for such a purpose a much greater number of +stars is necessary than can be incorporated in the ephemeris. + +From what I have said, it will be seen that the astronomical +tables, in general, do not satisfy the scientific condition of +completely representing observations to the last degree of +accuracy. Few, I think, have an idea how unsystematically work of +this kind has hitherto been performed. Until very lately the +tables we have possessed have been the work of one man here, +another there, and another one somewhere else, each using +different methods and different data. The result of this is that +there is nothing uniform and systematic among them, and that they +have every range of precision. This is no doubt due in part to the +fact that the construction of such tables, founded on the mass of +observation hitherto made, is entirely beyond the power of any one +man. What is wanted is a number of men of different degrees of +capacity, all co-operating on a uniform system, so as to obtain a +uniform result, like the astronomers in a large observatory. The +Greenwich Observatory presents an example of co-operative work of +this class extending over more than a century. But it has never +extended its operations far outside the field of observation, +reduction, and comparison with existing tables. It shows clearly, +from time to time, the errors of the tables used in the British +Nautical Almanac, but does nothing further, occasional +investigations excepted, in the way of supplying new tables. An +exception to this is a great work on the theory of the moon's +motion, in which Professor Airy is now engaged. + +It will be understood that several distinct conditions not yet +fulfilled are desirable in astronomical tables; one is that each +set of tables shall be founded on absolutely consistent data, for +instance, that the masses of the planets shall be the same +throughout. Another requirement is that this data shall be as near +the truth as astronomical data will suffice to determine them. The +third is that the results shall be correct in theory. That is, +whether they agree or disagree with observations, they shall be +such as result mathematically from the adopted data. + +Tables completely fulfilling these conditions are still a work of +the future. It is yet to be seen whether such co-operation as is +necessary to their production can be secured under any arrangement +whatever. + + + + + + +XIV + +THE WORLD'S DEBT TO ASTRONOMY + + +Astronomy is more intimately connected than any other science with +the history of mankind. While chemistry, physics, and we might say +all sciences which pertain to things on the earth, are +comparatively modern, we find that contemplative men engaged in +the study of the celestial motions even before the commencement of +authentic history. The earliest navigators of whom we know must +have been aware that the earth was round. This fact was certainly +understood by the ancient Greeks and Egyptians, as well as it is +at the present day. True, they did not know that the earth +revolved on its axis, but thought that the heavens and all that in +them is performed a daily revolution around our globe, which was, +therefore, the centre of the universe. It was the cynosure, or +constellation of the Little Bear, by which the sailors used to +guide their ships before the discovery of the mariner's compass. +Thus we see both a practical and contemplative side to astronomy +through all history. The world owes two debts to that science: one +for its practical uses, and the other for the ideas it has +afforded us of the immensity of creation. + +The practical uses of astronomy are of two kinds: One relates to +geography; the other to times, seasons, and chronology. Every +navigator who sails long out of sight of land must be something of +an astronomer. His compass tells him where are east, west, north, +and south, but it gives him no information as to where on the wide +ocean he may be, or whither the currents may be carrying him. Even +with the swiftest modern steamers it is not safe to trust to the +compass in crossing the Atlantic. A number of years ago the +steamer City of Washington set out on her usual voyage from +Liverpool to New York. By rare bad luck the weather was stormy or +cloudy during her whole passage, so that the captain could not get +a sight on the sun, and therefore had to trust to his compass and +his log-line, the former telling him in what direction he had +steamed, and the latter how fast he was going each hour. The +result was that the ship ran ashore on the coast of Nova Scotia, +when the captain thought he was approaching Nantucket. + +Not only the navigator but the surveyor in the western wilds must +depend on astronomical observations to learn his exact position on +the earth's surface, or the latitude and longitude of the camp +which he occupies. He is able to do this because the earth is +round, and the direction of the plumb-line not exactly the same at +any two places. Let us suppose that the earth stood still, so as +not to revolve on its axis at all. Then we should always see the +stars at rest and the star which was in the zenith of any place, +say a farm-house in New York, at any time, would be there every +night and every hour of the year. Now the zenith is simply the +point from which the plumb-line seems to drop. Lie on the ground; +hang a plummet above your head, sight on the line with one eye, +and the direction of the sight will be the zenith of your place. +Suppose the earth was still, and a certain star was at your +zenith. Then if you went to another place a mile away, the +direction of the plumb-line would be slightly different. The +change would, indeed, be very small, so small that you could not +detect it by sighting with the plumb-line. But astronomers and +surveyors have vastly more accurate instruments than the plumb- +line and the eye, instruments by which a deviation that the +unaided eye could not detect can be seen and measured. Instead of +the plumb-line they use a spirit-level or a basin of quicksilver. +The surface of quicksilver is exactly level and so at right angles +to the true direction of the plumb-line or the force of gravity. +Its direction is therefore a little different at two different +places on the surface, and the change can be measured by its +effect on the apparent direction of a star seen by reflection from +the surface. + +It is true that a considerable distance on the earth's surface +will seem very small in its effect on the position of a star. +Suppose there were two stars in the heavens, the one in the zenith +of the place where you now stand, and the other in the zenith of a +place a mile away. To the best eye unaided by a telescope those +two stars would look like a single one. But let the two places be +five miles apart, and the eye could see that there were two of +them. A good telescope could distinguish between two stars +corresponding to places not more than a hundred feet apart. The +most exact measurements can determine distances ranging from +thirty to sixty feet. If a skilful astronomical observer should +mount a telescope on your premises, and determine his latitude by +observations on two or three evenings, and then you should try to +trick him by taking up the instrument and putting it at another +point one hundred feet north or south, he would find out that +something was wrong by a single night's work. + +Within the past three years a wobbling of the earth's axis has +been discovered, which takes place within a circle thirty feet in +radius and sixty feet in diameter. Its effect was noticed in +astronomical observations many years ago, but the change it +produced was so small that men could not find out what the matter +was. The exact nature and amount of the wobbling is a work of the +exact astronomy of the present time. + +We cannot measure across oceans from island to island. Until a +recent time we have not even measured across the continent, from +New York to San Francisco, in the most precise way. Without +astronomy we should know nothing of the distance between New York +and Liverpool, except by the time which it took steamers to run +it, a measure which would be very uncertain indeed. But by the aid +of astronomical observations and the Atlantic cables the distance +is found within a few hundred yards. Without astronomy we could +scarcely make an accurate map of the United States, except at +enormous labor and expense, and even then we could not be sure of +its correctness. But the practical astronomer being able to +determine his latitude and longitude within fifty yards, the +positions of the principal points in all great cities of the +country are known, and can be laid down on maps. + +The world has always had to depend on astronomy for all its +knowledge concerning times and seasons. The changes of the moon +gave us the first month, and the year completes its round as the +earth travels in its orbit. The results of astronomical +observation are for us condensed into almanacs, which are now in +such universal use that we never think of their astronomical +origin. But in ancient times people had no almanacs, and they +learned the time of year, or the number of days in the year, by +observing the time when Sirius or some other bright star rose or +set with the sun, or disappeared from view in the sun's rays. At +Alexandria, in Egypt, the length of the year was determined yet +more exactly by observing when the sun rose exactly in the east +and set exactly in the west, a date which fixed the equinox for +them as for us. More than seventeen hundred years ago, Ptolemy, +the great author of The Almagest, had fixed the length of the year +to within a very few minutes. He knew it was a little less than +365 1/2 days. The dates of events in ancient history depend very +largely on the chronological cycles of astronomy. Eclipses of the +sun and moon sometimes fixed the date of great events, and we +learn the relation of ancient calendars to our own through the +motions of the earth and moon, and can thus measure out the years +for the events in ancient history on the same scale that we +measure out our own. + +At the present day, the work of the practical astronomer is made +use of in our daily life throughout the whole country in yet +another way. Our fore-fathers had to regulate their clocks by a +sundial, or perhaps by a mark at the corner of the house, which +showed where the shadow of the house fell at noon. Very rude +indeed was this method; and it was uncertain for another reason. +It is not always exactly twenty-four hours between two noons by +the sun, Sometimes for two or three months the sun will make it +noon earlier and earlier every day; and during several other +months later and later every day. The result is that, if a clock +is perfectly regulated, the sun will be sometimes a quarter of an +hour behind it, and sometimes nearly the same amount before it. +Any effort to keep the clock in accord with this changing sun was +in vain, and so the time of day was always uncertain. + +Now, however, at some of the principal observatories of the +country astronomical observations are made on every clear night +for the express purpose of regulating an astronomical clock with +the greatest exactness. Every day at noon a signal is sent to +various parts of the country by telegraph, so that all operators +and railway men who hear that signal can set their clock at noon +within two or three seconds. People who live near railway stations +can thus get their time from it, and so exact time is diffused +into every household of the land which is at all near a railway +station, without the trouble of watching the sun. Thus increased +exactness is given to the time on all our railroads, increased +safety is obtained, and great loss of time saved to every one. If +we estimated the money value of this saving alone we should no +doubt find it to be greater than all that our study of astronomy +costs. + +It must therefore be conceded that, on the whole, astronomy is a +science of more practical use than one would at first suppose. To +the thoughtless man, the stars seem to have very little relation +to his daily life; they might be forever hid from view without his +being the worse for it. He wonders what object men can have in +devoting themselves to the study of the motions or phenomena of +the heavens. But the more he looks into the subject, and the wider +the range which his studies include, the more he will be impressed +with the great practical usefulness of the science of the heavens. +And yet I think it would be a serious error to say that the +world's greatest debt to astronomy was owing to its usefulness in +surveying, navigation, and chronology. The more enlightened a man +is, the more he will feel that what makes his mind what it is, and +gives him the ideas of himself and creation which he possesses, is +more important than that which gains him wealth. I therefore hold +that the world's greatest debt to astronomy is that it has taught +us what a great thing creation is, and what an insignificant part +of the Creator's work is this earth on which we dwell, and +everything that is upon it. That space is infinite, that wherever +we go there is a farther still beyond it, must have been accepted +as a fact by all men who have thought of the subject since men +began to think at all. But it is very curious how hard even the +astronomers found it to believe that creation is as large as we +now know it to be. The Greeks had their gods on or not very far +above Olympus, which was a sort of footstool to the heavens. +Sometimes they tried to guess how far it probably was from the +vault of heaven to the earth, and they had a myth as to the time +it took Vulcan to fall. Ptolemy knew that the moon was about +thirty diameters of the earth distant from us, and he knew that +the sun was many times farther than the moon; he thought it about +twenty times as far, but could not be sure. We know that it is +nearly four hundred times as far. + +When Copernicus propounded the theory that the earth moved around +the sun, and not the sun around the earth, he was able to fix the +relative distances of the several planets, and thus make a map of +the solar system. But he knew nothing about the scale of this map. +He knew, for example, that Venus was a little more than two-thirds +the distance of the earth from the sun, and that Mars was about +half as far again as the earth, Jupiter about five times, and +Saturn about ten times; but he knew nothing about the distance of +any one of them from the sun. He had his map all right, but he +could not give any scale of miles or any other measurements upon +it. The astronomers who first succeeded him found that the +distance was very much greater than had formerly been supposed; +that it was, in fact, for them immeasurably great, and that was +all they could say about it. + +The proofs which Copernicus gave that the earth revolved around +the sun were so strong that none could well doubt them. And yet +there was a difficulty in accepting the theory which seemed +insuperable. If the earth really moved in so immense an orbit as +it must, then the stars would seem to move in the opposite +direction, just as, if you were in a train that is shunting off +cars one after another, as the train moves back and forth you see +its motion in the opposite motion of every object around you. If +then the earth at one side of its orbit was exactly between two +stars, when it moved to the other side of its orbit it would not +be in a line between them, but each star would have seemed to move +in the opposite direction. + +For centuries astronomers made the most exact observations that +they were able without having succeeded in detecting any such +apparent motion among the stars. Here was a mystery which they +could not solve. Either the Copernican system was not true, after +all, and the earth did not move in an orbit, or the stars were at +such immense distances that the whole immeasurable orbit of the +earth is a mere point in comparison. Philosophers could not +believe that the Creator would waste room by allowing the +inconceivable spaces which appeared to lie between our system and +the fixed stars to remain unused, and so thought there must be +something wrong in the theory of the earth's motion. + +Not until the nineteenth century was well in progress did the most +skilful observers of their time, Bessel and Struve, having at +command the most refined instruments which science was then able +to devise, discover the reality of the parallax of the stars, and +show that the nearest of these bodies which they could find was +more than 400,000 times as far as the 93,000,000 of miles which +separate the earth from the sun. During the half-century and more +which has elapsed since this discovery, astronomers have been +busily engaged in fathoming the heavenly depths. The nearest star +they have been able to find is about 280,000 times the sun's +distance. A dozen or a score more are within 1,000,000 times that +distance. Beyond this all is unfathomable by any sounding-line yet +known to man. + +The results of these astronomical measures are stupendous beyond +conception. No mere statement in numbers conveys any idea of it. +Nearly all the brighter stars are known to be flying through space +at speeds which generally range between ten and forty or fifty +miles per second, some slower and some swifter, even up to one or +two hundred miles a second. Such a speed would carry us across the +Atlantic while we were reading two or three of these sentences. +These motions take place some in one direction and some in +another. Some of the stars are coming almost straight towards us. +Should they reach us, and pass through our solar system, the +result would be destructive to our earth, and perhaps to our sun. + +Are we in any danger? No, because, however madly they may come, +whether ten, twenty, or one hundred miles per second, so many +millions of years must elapse before they reach us that we need +give ourselves no concern in the matter. Probably none of them are +coming straight to us; their course deviates just a hair's-breadth +from our system, but that hair's-breadth is so large a quantity +that when the millions of years elapse their course will lie on +one side or the other of our system and they will do no harm to +our planet; just as a bullet fired at an insect a mile away would +be nearly sure to miss it in one direction or the other. + +Our instrument makers have constructed telescopes more and more +powerful, and with these the whole number of stars visible is +carried up into the millions, say perhaps to fifty or one hundred +millions. For aught we know every one of those stars may have +planets like our own circling round it, and these planets may be +inhabited by beings equal to ourselves. To suppose that our globe +is the only one thus inhabited is something so unlikely that no +one could expect it. It would be very nice to know something about +the people who may inhabit these bodies, but we must await our +translation to another sphere before we can know anything on the +subject. Meanwhile, we have gained what is of more value than gold +or silver; we have learned that creation transcends all our +conceptions, and our ideas of its Author are enlarged accordingly. + + + + + +XV + +AN ASTRONOMICAL FRIENDSHIP + + +There are few men with whom I would like so well to have a quiet +talk as with Father Hell. I have known more important and more +interesting men, but none whose acquaintance has afforded me a +serener satisfaction, or imbued me with an ampler measure of a +feeling that I am candid enough to call self-complacency. The ties +that bind us are peculiar. When I call him my friend, I do not +mean that we ever hobnobbed together. But if we are in sympathy, +what matters it that he was dead long before I was born, that he +lived in one century and I in another? Such differences of +generation count for little in the brotherhood of astronomy, the +work of whose members so extends through all time that one might +well forget that he belongs to one century or to another. + +Father Hell was an astronomer. Ask not whether he was a very great +one, for in our science we have no infallible gauge by which we +try men and measure their stature. He was a lover of science and +an indefatigable worker, and he did what in him lay to advance our +knowledge of the stars. Let that suffice. I love to fancy that in +some other sphere, either within this universe of ours or outside +of it, all who have successfully done this may some time gather +and exchange greetings. Should this come about there will be a +few--Hipparchus and Ptolemy, Copernicus and Newton, Galileo and +Herschel--to be surrounded by admiring crowds. But these men will +have as warm a grasp and as kind a word for the humblest of their +followers, who has merely discovered a comet or catalogued a +nebula, as for the more brilliant of their brethren. + +My friend wrote the letters S. J. after his name. This would +indicate that he had views and tastes which, in some points, were +very different from my own. But such differences mark no dividing +line in the brotherhood of astronomy. My testimony would count for +nothing were I called as witness for the prosecution in a case +against the order to which my friend belonged. The record would be +very short: Deponent saith that he has at various times known +sundry members of the said order; and that they were lovers of +sound learning, devoted to the discovery and propagation of +knowledge; and further deponent saith not. + +If it be true that an undevout astronomer is mad, then was Father +Hell the sanest of men. In his diary we find entries like these: +"Benedicente Deo, I observed the Sun on the meridian to-day.... +Deo quoque benedicente, I to-day got corresponding altitudes of +the Sun's upper limb." How he maintained the simplicity of his +faith in the true spirit of the modern investigator is shown by +his proceedings during a momentous voyage along the coast of +Norway, of which I shall presently speak. He and his party were +passengers on a Norwegian vessel. For twelve consecutive days they +had been driven about by adverse storms, threatened with shipwreck +on stony cliffs, and finally compelled to take refuge in a little +bay, with another ship bound in the same direction, there to wait +for better weather. + +Father Hell was philosopher enough to know that unusual events do +not happen without cause. Perhaps he would have undergone a week +of storm without its occurring to him to investigate the cause of +such a bad spell of weather. But when he found the second week +approaching its end and yet no sign of the sun appearing or the +wind abating, he was satisfied that something must be wrong. So he +went to work in the spirit of the modern physician who, when there +is a sudden outbreak of typhoid fever, looks at the wells and +examines their water with the microscope to find the microbes +that must be lurking somewhere. He looked about, and made careful +inquiries to find what wickedness captain and crew had been guilty +of to bring such a punishment. Success soon rewarded his efforts. +The King of Denmark had issued a regulation that no fish or oil +should be sold along the coast except by the regular dealers in +those articles. And the vessel had on board contraband fish and +blubber, to be disposed of in violation of this law. + +The astronomer took immediate and energetic measures to insure the +public safety. He called the crew together, admonished them of +their sin, the suffering they were bringing on themselves, and the +necessity of getting back to their families. He exhorted them to +throw the fish overboard, as the only measure to secure their +safety. In the goodness of his heart, he even offered to pay the +value of the jettison as soon as the vessel reached Drontheim. + +But the descendants of the Vikings were stupid and unenlightened +men--"educatione sua et professione homines crassissimi"--and +would not swallow the medicine so generously offered. They claimed +that, as they had bought the fish from the Russians, their +proceedings were quite lawful. As for being paid to throw the fish +overboard, they must have spot cash in advance or they would not +do it. + +After further fruitless conferences, Father Hell determined to +escape the danger by transferring his party to the other vessel. +They had not more than got away from the wicked crew than Heaven +began to smile on their act--"factum comprobare Deus ipse +videtur"--the clouds cleared away, the storm ceased to rage, and +they made their voyage to Copenhagen under sunny skies. I regret +to say that the narrative is silent as to the measure of storm +subsequently awarded to the homines crassissimi of the forsaken +vessel. + +For more than a century Father Hell had been a well-known figure +in astronomical history. His celebrity was not, however, of such a +kind as the Royal Astronomer of Austria that he was ought to +enjoy. A not unimportant element in his fame was a suspicion of +his being a black sheep in the astronomical flock. He got under +this cloud through engaging in a trying and worthy enterprise. On +June 3, 1769, an event occurred which had for generations been +anticipated with the greatest interest by the whole astronomical +world. This was a transit of Venus over the disk of the sun. Our +readers doubtless know that at that time such a transit afforded +the most accurate method known of determining the distance of the +earth from the sun. To attain this object, parties were sent to +the most widely separated parts of the globe, not only over wide +stretches of longitude, but as near as possible to the two poles +of the earth. One of the most favorable and important regions of +observation was Lapland, and the King of Denmark, to whom that +country then belonged, interested himself in getting a party sent +thither. After a careful survey of the field he selected Father +Hell, Chief of the Observatory at Vienna, and well known as editor +and publisher of an annual ephemeris, in which the movements and +aspects of the heavenly bodies were predicted. The astronomer +accepted the mission and undertook what was at that time a rather +hazardous voyage. His station was at Vardo in the region of the +North Cape. What made it most advantageous for the purpose was its +being situated several degrees within the Arctic Circle, so that +on the date of the transit the sun did not set. The transit began +when the sun was still two or three hours from his midnight goal, +and it ended nearly an equal time afterwards. The party consisted +of Hell himself, his friend and associate, Father Sajnovics, one +Dominus Borgrewing, of whom history, so far as I know, says +nothing more, and an humble individual who in the record receives +no other designation than "Familias." This implies, we may +suppose, that he pitched the tent and made the coffee. If he did +nothing but this we might pass him over in silence. But we learn +that on the day of the transit he stood at the clock and counted +the all-important seconds while the observations were going on. + +The party was favored by cloudless weather, and made the required +observations with entire success. They returned to Copenhagen, and +there Father Hell remained to edit and publish his work. +Astronomers were naturally anxious to get the results, and showed +some impatience when it became known that Hell refused to announce +them until they were all reduced and printed in proper form under +the auspices of his royal patron. While waiting, the story got +abroad that he was delaying the work until he got the results of +observations made elsewhere, in order to "doctor" his own and make +them fit in with the others. One went so far as to express a +suspicion that Hell had not seen the transit at all, owing to +clouds, and that what he pretended to publish were pure +fabrications. But his book came out in a few months in such good +form that this suspicion was evidently groundless. Still, the +fears that the observations were not genuine were not wholly +allayed, and the results derived from them were, in consequence, +subject to some doubt. Hell himself considered the reflections +upon his integrity too contemptible to merit a serious reply. It +is said that he wrote to some one offering to exhibit his journal +free from interlineations or erasures, but it does not appear that +there is any sound authority for this statement. What is of some +interest is that he published a determination of the parallax of +the sun based on the comparison of his own observations with those +made at other stations. The result was 8".70. It was then, and +long after, supposed that the actual value of the parallax was +about 8".50, and the deviation of Hell's result from this was +considered to strengthen the doubt as to the correctness of his +work. It is of interest to learn that, by the most recent +researches, the number in question must be between 8".75 and +8".80, so that in reality Hell's computations came nearer the +truth than those generally current during the century following +his work. + +Thus the matter stood for sixty years after the transit, and for a +generation after Father Hell had gone to his rest. About 1830 it +was found that the original journal of his voyage, containing the +record of his work as first written down at the station, was still +preserved at the Vienna Observatory. Littrow, then an astronomer +at Vienna, made a critical examination of this record in order to +determine whether it had been tampered with. His conclusions were +published in a little book giving a transcript of the journal, a +facsimile of the most important entries, and a very critical +description of the supposed alterations made in them. He reported +in substance that the original record had been so tampered with +that it was impossible to decide whether the observations as +published were genuine or not. The vital figures, those which told +the times when Venus entered upon the sun, had been erased, and +rewritten with blacker ink. This might well have been done after +the party returned to Copenhagen. The case against the observer +seemed so well made out that professors of astronomy gave their +hearers a lesson in the value of truthfulness, by telling them how +Father Hell had destroyed what might have been very good +observations by trying to make them appear better than they really +were. + +In 1883 I paid a visit to Vienna for the purpose of examining the +great telescope which had just been mounted in the observatory +there by Grubb, of Dublin. The weather was so unfavorable that it +was necessary to remain two weeks, waiting for an opportunity to +see the stars. One evening I visited the theatre to see Edwin +Booth, in his celebrated tour over the Continent, play King Lear +to the applauding Viennese. But evening amusements cannot be +utilized to kill time during the day. Among the works I had +projected was that of rediscussing all the observations made on +the transits of Venus which had occurred in 1761 and 1769, by the +light of modern discovery. As I have already remarked, Hell's +observations were among the most important made, if they were only +genuine. So, during my almost daily visits to the observatory, I +asked permission of the director to study Hell's manuscript, which +was deposited in the library of the institution. Permission was +freely given, and for some days I pored over the manuscript. It is +a very common experience in scientific research that a subject +which seems very unpromising when first examined may be found more +and more interesting as one looks further into it. Such was the +case here. For some time there did not seem any possibility of +deciding the question whether the record was genuine. But every +time I looked at it some new point came to light. I compared the +pages with Littrow's published description and was struck by a +seeming want of precision, especially when he spoke of the ink +with which the record had been made. Erasers were doubtless +unknown in those days--at least our astronomer had none on his +expedition--so when he found he had written the wrong word he +simply wiped the place off with, perhaps, his finger and wrote +what he wanted to say. In such a case Littrow described the matter +as erased and new matter written. When the ink flowed freely from +the quill pen it was a little dark. Then Littrow said a different +kind of ink had been used, probably after he had got back from his +journey. On the other hand, there was a very singular case in +which there had been a subsequent interlineation in ink of quite a +different tint, which Littrow said nothing about. This seemed so +curious that I wrote in my notes as follows: + +"That Littrow, in arraying his proofs of Hell's forgery, should +have failed to dwell upon the obvious difference between this ink +and that with which the alterations were made leads me to suspect +a defect in his sense of color." + +The more I studied the description and the manuscript the stronger +this impression became. Then it occurred to me to inquire whether +perhaps such could have been the case. So I asked Director Weiss +whether anything was known as to the normal character of Littrow's +power of distinguishing colors. His answer was prompt and +decisive. "Oh yes, Littrow was color-blind to red. He could not +distinguish between the color of Aldebaran and the whitest star." +No further research was necessary. For half a century the +astronomical world had based an impression on the innocent but +mistaken evidence of a color-blind man--respecting the tints of +ink in a manuscript. + +It has doubtless happened more than once that when an intimate +friend has suddenly and unexpectedly passed away, the reader has +ardently wished that it were possible to whisper just one word of +appreciation across the dark abyss. And so it is that I have ever +since felt that I would like greatly to tell Father Hell the story +of my work at Vienna in 1883. + + + + + +XVI + +THE EVOLUTION OF THE SCIENTIFIC INVESTIGATOR + +[Footnote: Presidential address at the opening of the +International Congress of Arts and Science, St. Louis Exposition, +September 21: 1904.] + + +As we look at the assemblage gathered in this hall, comprising so +many names of widest renown in every branch of learning--we might +almost say in every field of human endeavor--the first inquiry +suggested must be after the object of our meeting. The answer is +that our purpose corresponds to the eminence of the assemblage. We +aim at nothing less than a survey of the realm of knowledge, as +comprehensive as is permitted by the limitations of time and +space. The organizers of our congress have honored me with the +charge of presenting such preliminary view of its field as may +make clear the spirit of our undertaking. + +Certain tendencies characteristic of the science of our day +clearly suggest the direction of our thoughts most appropriate to +the occasion. Among the strongest of these is one towards laying +greater stress on questions of the beginnings of things, and +regarding a knowledge of the laws of development of any object of +study as necessary to the understanding of its present form. It +may be conceded that the principle here involved is as applicable +in the broad field before us as in a special research into the +properties of the minutest organism. It therefore seems meet that +we should begin by inquiring what agency has brought about the +remarkable development of science to which the world of to-day +bears witness. This view is recognized in the plan of our +proceedings by providing for each great department of knowledge a +review of its progress during the century that has elapsed since +the great event commemorated by the scenes outside this hall. But +such reviews do not make up that general survey of science at +large which is necessary to the development of our theme, and +which must include the action of causes that had their origin long +before our time. The movement which culminated in making the +nineteenth century ever memorable in history is the outcome of a +long series of causes, acting through many centuries, which are +worthy of especial attention on such an occasion as this. In +setting them forth we should avoid laying stress on those visible +manifestations which, striking the eye of every beholder, are in +no danger of being overlooked, and search rather for those +agencies whose activities underlie the whole visible scene, but +which are liable to be blotted out of sight by the very brilliancy +of the results to which they have given rise. It is easy to draw +attention to the wonderful qualities of the oak; but, from that +very fact, it may be needful to point out that the real wonder +lies concealed in the acorn from which it grew. + +Our inquiry into the logical order of the causes which have made +our civilization what it is to-day will be facilitated by bringing +to mind certain elementary considerations--ideas so familiar that +setting them forth may seem like citing a body of truisms--and yet +so frequently overlooked, not only individually, but in their +relation to each other, that the conclusion to which they lead may +be lost to sight. One of these propositions is that psychical +rather than material causes are those which we should regard as +fundamental in directing the development of the social organism. +The human intellect is the really active agent in every branch of +endeavor--the primum mobile of civilization--and all those +material manifestations to which our attention is so often +directed are to be regarded as secondary to this first agency. If +it be true that "in the world is nothing great but man; in man is +nothing great but mind," then should the key-note of our discourse +be the recognition of this first and greatest of powers. + +Another well-known fact is that those applications of the forces +of nature to the promotion of human welfare which have made our +age what it is are of such comparatively recent origin that we +need go back only a single century to antedate their most +important features, and scarcely more than four centuries to find +their beginning. It follows that the subject of our inquiry should +be the commencement, not many centuries ago, of a certain new form +of intellectual activity. + +Having gained this point of view, our next inquiry will be into +the nature of that activity and its relation to the stages of +progress which preceded and followed its beginning. The +superficial observer, who sees the oak but forgets the acorn, +might tell us that the special qualities which have brought out +such great results are expert scientific knowledge and rare +ingenuity, directed to the application of the powers of steam and +electricity. From this point of view the great inventors and the +great captains of industry were the first agents in bringing about +the modern era. But the more careful inquirer will see that the +work of these men was possible only through a knowledge of the +laws of nature, which had been gained by men whose work took +precedence of theirs in logical order, and that success in +invention has been measured by completeness in such knowledge. +While giving all due honor to the great inventors, let us remember +that the first place is that of the great investigators, whose +forceful intellects opened the way to secrets previously hidden +from men. Let it be an honor and not a reproach to these men that +they were not actuated by the love of gain, and did not keep +utilitarian ends in view in the pursuit of their researches. If it +seems that in neglecting such ends they were leaving undone the +most important part of their work, let us remember that Nature +turns a forbidding face to those who pay her court with the hope +of gain, and is responsive only to those suitors whose love for +her is pure and undefiled. Not only is the special genius required +in the investigator not that generally best adapted to applying +the discoveries which he makes, but the result of his having +sordid ends in view would be to narrow the field of his efforts, +and exercise a depressing effect upon his activities. The true man +of science has no such expression in his vocabulary as "useful +knowledge." His domain is as wide as nature itself, and he best +fulfils his mission when he leaves to others the task of applying +the knowledge he gives to the world. + +We have here the explanation of the well-known fact that the +functions of the investigator of the laws of nature, and of the +inventor who applies these laws to utilitarian purposes, are +rarely united in the same person. If the one conspicuous exception +which the past century presents to this rule is not unique, we +should probably have to go back to Watt to find another. + +From this view-point it is clear that the primary agent in the +movement which has elevated man to the masterful position he now +occupies is the scientific investigator. He it is whose work has +deprived plague and pestilence of their terrors, alleviated human +suffering, girdled the earth with the electric wire, bound the +continent with the iron way, and made neighbors of the most +distant nations. As the first agent which has made possible this +meeting of his representatives, let his evolution be this day our +worthy theme. As we follow the evolution of an organism by +studying the stages of its growth, so we have to show how the work +of the scientific investigator is related to the ineffectual +efforts of his predecessors. + +In our time we think of the process of development in nature as +one going continuously forward through the combination of the +opposite processes of evolution and dissolution. The tendency of +our thought has been in the direction of banishing cataclysms to +the theological limbo, and viewing Nature as a sleepless plodder, +endowed with infinite patience, waiting through long ages for +results. I do not contest the truth of the principle of continuity +on which this view is based. But it fails to make known to us the +whole truth. The building of a ship from the time that her keel is +laid until she is making her way across the ocean is a slow and +gradual process; yet there is a cataclysmic epoch opening up a new +era in her history. It is the moment when, after lying for months +or years a dead, inert, immovable mass, she is suddenly endowed +with the power of motion, and, as if imbued with life, glides into +the stream, eager to begin the career for which she was designed. + +I think it is thus in the development of humanity. Long ages may +pass during which a race, to all external observation, appears to +be making no real progress. Additions may be made to learning, and +the records of history may constantly grow, but there is nothing +in its sphere of thought, or in the features of its life, that can +be called essentially new. Yet, Nature may have been all along +slowly working in a way which evades our scrutiny, until the +result of her operations suddenly appears in a new and +revolutionary movement, carrying the race to a higher plane of +civilization. + +It is not difficult to point out such epochs in human progress. +The greatest of all, because it was the first, is one of which we +find no record either in written or geological history. It was the +epoch when our progenitors first took conscious thought of the +morrow, first used the crude weapons which Nature had placed +within their reach to kill their prey, first built a fire to warm +their bodies and cook their food. I love to fancy that there was +some one first man, the Adam of evolution, who did all this, and +who used the power thus acquired to show his fellows how they +might profit by his example. When the members of the tribe or +community which he gathered around him began to conceive of life +as a whole--to include yesterday, to-day, and to-morrow in the +same mental grasp--to think how they might apply the gifts of +Nature to their own uses--a movement was begun which should +ultimately lead to civilization. + +Long indeed must have been the ages required for the development +of this rudest primitive community into the civilization revealed +to us by the most ancient tablets of Egypt and Assyria. After +spoken language was developed, and after the rude representation +of ideas by visible marks drawn to resemble them had long been +practised, some Cadmus must have invented an alphabet. When the +use of written language was thus introduced, the word of command +ceased to be confined to the range of the human voice, and it +became possible for master minds to extend their influence as far +as a written message could be carried. Then were communities +gathered into provinces; provinces into kingdoms, kingdoms into +great empires of antiquity. Then arose a stage of civilization +which we find pictured in the most ancient records--a stage in +which men were governed by laws that were perhaps as wisely +adapted to their conditions as our laws are to ours--in which the +phenomena of nature were rudely observed, and striking occurrences +in the earth or in the heavens recorded in the annals of the +nation. + +Vast was the progress of knowledge during the interval between +these empires and the century in which modern science began. Yet, +if I am right in making a distinction between the slow and regular +steps of progress, each growing naturally out of that which +preceded it, and the entrance of the mind at some fairly definite +epoch into an entirely new sphere of activity, it would appear +that there was only one such epoch during the entire interval. +This was when abstract geometrical reasoning commenced, and +astronomical observations aiming at precision were recorded, +compared, and discussed. Closely associated with it must have been +the construction of the forms of logic. The radical difference +between the demonstration of a theorem of geometry and the +reasoning of every-day life which the masses of men must have +practised from the beginning, and which few even to-day ever get +beyond, is so evident at a glance that I need not dwell upon it. +The principal feature of this advance is that, by one of those +antinomies of human intellect of which examples are not wanting +even in our own time, the development of abstract ideas preceded +the concrete knowledge of natural phenomena. When we reflect that +in the geometry of Euclid the science of space was brought to such +logical perfection that even to-day its teachers are not agreed as +to the practicability of any great improvement upon it, we cannot +avoid the feeling that a very slight change in the direction of +the intellectual activity of the Greeks would have led to the +beginning of natural science. But it would seem that the very +purity and perfection which was aimed at in their system of +geometry stood in the way of any extension or application of its +methods and spirit to the field of nature. One example of this is +worthy of attention. In modern teaching the idea of magnitude as +generated by motion is freely introduced. A line is described by a +moving point; a plane by a moving line; a solid by a moving plane. +It may, at first sight, seem singular that this conception finds +no place in the Euclidian system. But we may regard the omission +as a mark of logical purity and rigor. Had the real or supposed +advantages of introducing motion into geometrical conceptions been +suggested to Euclid, we may suppose him to have replied that the +theorems of space are independent of time; that the idea of motion +necessarily implies time, and that, in consequence, to avail +ourselves of it would be to introduce an extraneous element into +geometry. + +It is quite possible that the contempt of the ancient philosophers +for the practical application of their science, which has +continued in some form to our own time, and which is not +altogether unwholesome, was a powerful factor in the same +direction. The result was that, in keeping geometry pure from +ideas which did not belong to it, it failed to form what might +otherwise have been the basis of physical science. Its founders +missed the discovery that methods similar to those of geometric +demonstration could be extended into other and wider fields than +that of space. Thus not only the development of applied geometry +but the reduction of other conceptions to a rigorous mathematical +form was indefinitely postponed. + +There is, however, one science which admitted of the immediate +application of the theorems of geometry, and which did not require +the application of the experimental method. Astronomy is +necessarily a science of observation pure and simple, in which +experiment can have no place except as an auxiliary. The vague +accounts of striking celestial phenomena handed down by the +priests and astrologers of antiquity were followed in the time of +the Greeks by observations having, in form at least, a rude +approach to precision, though nothing like the degree of precision +that the astronomer of to-day would reach with the naked eye, +aided by such instruments as he could fashion from the tools at +the command of the ancients. + +The rude observations commenced by the Babylonians were continued +with gradually improving instruments--first by the Greeks and +afterwards by the Arabs--but the results failed to afford any +insight into the true relation of the earth to the heavens. What +was most remarkable in this failure is that, to take a first step +forward which would have led on to success, no more was necessary +than a course of abstract thinking vastly easier than that +required for working out the problems of geometry. That space is +infinite is an unexpressed axiom, tacitly assumed by Euclid and +his successors. Combining this with the most elementary +consideration of the properties of the triangle, it would be seen +that a body of any given size could be placed at such a distance +in space as to appear to us like a point. Hence a body as large as +our earth, which was known to be a globe from the time that the +ancient Phoenicians navigated the Mediterranean, if placed in the +heavens at a sufficient distance, would look like a star. The +obvious conclusion that the stars might be bodies like our globe, +shining either by their own light or by that of the sun, would +have been a first step to the understanding of the true system of +the world. + +There is historic evidence that this deduction did not wholly +escape the Greek thinkers. It is true that the critical student +will assign little weight to the current belief that the vague +theory of Pythagoras--that fire was at the centre of all things-- +implies a conception of the heliocentric theory of the solar +system. But the testimony of Archimedes, confused though it is in +form, leaves no serious doubt that Aristarchus of Samos not only +propounded the view that the earth revolves both on its own axis +and around the sun, but that he correctly removed the great +stumbling-block in the way of this theory by adding that the +distance of the fixed stars was infinitely greater than the +dimensions of the earth's orbit. Even the world of philosophy was +not yet ready for this conception, and, so far from seeing the +reasonableness of the explanation, we find Ptolemy arguing against +the rotation of the earth on grounds which careful observations of +the phenomena around him would have shown to be ill-founded. + +Physical science, if we can apply that term to an uncoordinated +body of facts, was successfully cultivated from the earliest +times. Something must have been known of the properties of metals, +and the art of extracting them from their ores must have been +practised, from the time that coins and medals were first stamped. +The properties of the most common compounds were discovered by +alchemists in their vain search for the philosopher's stone, but +no actual progress worthy of the name rewarded the practitioners +of the black art. + +Perhaps the first approach to a correct method was that of +Archimedes, who by much thinking worked out the law of the lever, +reached the conception of the centre of gravity, and demonstrated +the first principles of hydrostatics. It is remarkable that he did +not extend his researches into the phenomena of motion, whether +spontaneous or produced by force. The stationary condition of the +human intellect is most strikingly illustrated by the fact that +not until the time of Leonardo was any substantial advance made on +his discovery. To sum up in one sentence the most characteristic +feature of ancient and medieval science, we see a notable contrast +between the precision of thought implied in the construction and +demonstration of geometrical theorems and the vague indefinite +character of the ideas of natural phenomena generally, a contrast +which did not disappear until the foundations of modern science +began to be laid. + +We should miss the most essential point of the difference between +medieval and modern learning if we looked upon it as mainly a +difference either in the precision or the amount of knowledge. The +development of both of these qualities would, under any +circumstances, have been slow and gradual, but sure. We can hardly +suppose that any one generation, or even any one century, would +have seen the complete substitution of exact for inexact ideas. +Slowness of growth is as inevitable in the case of knowledge as in +that of a growing organism. The most essential point of difference +is one of those seemingly slight ones, the importance of which we +are too apt to overlook. It was like the drop of blood in the +wrong place, which some one has told us makes all the difference +between a philosopher and a maniac. It was all the difference +between a living tree and a dead one, between an inert mass and a +growing organism. The transition of knowledge from the dead to the +living form must, in any complete review of the subject, be looked +upon as the really great event of modern times. Before this event +the intellect was bound down by a scholasticism which regarded +knowledge as a rounded whole, the parts of which were written in +books and carried in the minds of learned men. The student was +taught from the beginning of his work to look upon authority as +the foundation of his beliefs. The older the authority the greater +the weight it carried. So effective was this teaching that it +seems never to have occurred to individual men that they had all +the opportunities ever enjoyed by Aristotle of discovering truth, +with the added advantage of all his knowledge to begin with. +Advanced as was the development of formal logic, that practical +logic was wanting which could see that the last of a series of +authorities, every one of which rested on those which preceded it, +could never form a surer foundation for any doctrine than that +supplied by its original propounder. + +The result of this view of knowledge was that, although during the +fifteen centuries following the death of the geometer of Syracuse +great universities were founded at which generations of professors +expounded all the learning of their time, neither professor nor +student ever suspected what latent possibilities of good were +concealed in the most familiar operations of Nature. Every one +felt the wind blow, saw water boil, and heard the thunder crash, +but never thought of investigating the forces here at play. Up to +the middle of the fifteenth century the most acute observer could +scarcely have seen the dawn of a new era. + +In view of this state of things it must be regarded as one of the +most remarkable facts in evolutionary history that four or five +men, whose mental constitution was either typical of the new order +of things, or who were powerful agents in bringing it about, were +all born during the fifteenth century, four of them at least, at +so nearly the same time as to be contemporaries. + +Leonardo da Vinci, whose artistic genius has charmed succeeding +generations, was also the first practical engineer of his time, +and the first man after Archimedes to make a substantial advance +in developing the laws of motion. That the world was not prepared +to make use of his scientific discoveries does not detract from +the significance which must attach to the period of his birth. + +Shortly after him was born the great navigator whose bold spirit +was to make known a new world, thus giving to commercial +enterprise that impetus which was so powerful an agent in bringing +about a revolution in the thoughts of men. + +The birth of Columbus was soon followed by that of Copernicus, the +first after Aristarchus to demonstrate the true system of the +world. In him more than in any of his contemporaries do we see the +struggle between the old forms of thought and the new. It seems +almost pathetic and is certainly most suggestive of the general +view of knowledge taken at that time that, instead of claiming +credit for bringing to light great truths before unknown, he made +a labored attempt to show that, after all, there was nothing +really new in his system, which he claimed to date from Pythagoras +and Philolaus. In this connection it is curious that he makes no +mention of Aristarchus, who I think will be regarded by +conservative historians as his only demonstrated predecessor. To +the hold of the older ideas upon his mind we must attribute the +fact that in constructing his system he took great pains to make +as little change as possible in ancient conceptions. + +Luther, the greatest thought-stirrer of them all, practically of +the same generation with Copernicus, Leonardo and Columbus, does +not come in as a scientific investigator, but as the great +loosener of chains which had so fettered the intellect of men that +they dared not think otherwise than as the authorities thought. + +Almost coeval with the advent of these intellects was the +invention of printing with movable type. Gutenberg was born during +the first decade of the century, and his associates and others +credited with the invention not many years afterwards. If we +accept the principle on which I am basing my argument, that in +bringing out the springs of our progress we should assign the +first place to the birth of those psychic agencies which started +men on new lines of thought, then surely was the fifteenth the +wonderful century. + +Let us not forget that, in assigning the actors then born to their +places, we are not narrating history, but studying a special phase +of evolution. It matters not for us that no university invited +Leonardo to its halls, and that his science was valued by his +contemporaries only as an adjunct to the art of engineering. The +great fact still is that he was the first of mankind to propound +laws of motion. It is not for anything in Luther's doctrines that +he finds a place in our scheme. No matter for us whether they were +sound or not. What he did towards the evolution of the scientific +investigator was to show by his example that a man might question +the best-established and most venerable authority and still live-- +still preserve his intellectual integrity--still command a hearing +from nations and their rulers. It matters not for us whether +Columbus ever knew that he had discovered a new continent. His +work was to teach that neither hydra, chimera nor abyss--neither +divine injunction nor infernal machination--was in the way of men +visiting every part of the globe, and that the problem of +conquering the world reduced itself to one of sails and rigging, +hull and compass. The better part of Copernicus was to direct man +to a view-point whence he should see that the heavens were of like +matter with the earth. All this done, the acorn was planted from +which the oak of our civilization should spring. The mad quest for +gold which followed the discovery of Columbus, the questionings +which absorbed the attention of the learned, the indignation +excited by the seeming vagaries of a Paracelsus, the fear and +trembling lest the strange doctrine of Copernicus should undermine +the faith of centuries, were all helps to the germination of the +seed--stimuli to thought which urged it on to explore the new +fields opened up to its occupation. This given, all that has since +followed came out in regular order of development, and need be +here considered only in those phases having a special relation to +the purpose of our present meeting. + +So slow was the growth at first that the sixteenth century may +scarcely have recognized the inauguration of a new era. Torricelli +and Benedetti were of the third generation after Leonardo, and +Galileo, the first to make a substantial advance upon his theory, +was born more than a century after him. Only two or three men +appeared in a generation who, working alone, could make real +progress in discovery, and even these could do little in leavening +the minds of their fellowmen with the new ideas. + +Up to the middle of the seventeenth century an agent which all +experience since that time shows to be necessary to the most +productive intellectual activity was wanting. This was the +attrition of like minds, making suggestions to one another, +criticising, comparing, and reasoning. This element was introduced +by the organization of the Royal Society of London and the Academy +of Sciences of Paris. + +The members of these two bodies seem like ingenious youth suddenly +thrown into a new world of interesting objects, the purposes and +relations of which they had to discover. The novelty of the +situation is strikingly shown in the questions which occupied the +minds of the incipient investigators. One natural result of +British maritime enterprise was that the aspirations of the +Fellows of the Royal Society were not confined to any continent or +hemisphere. Inquiries were sent all the way to Batavia to know +"whether there be a hill in Sumatra which burneth continually, and +a fountain which runneth pure balsam." The astronomical precision +with which it seemed possible that physiological operations might +go on was evinced by the inquiry whether the Indians can so +prepare that stupefying herb Datura that "they make it lie several +days, months, years, according as they will, in a man's body without +doing him any harm, and at the end kill him without missing an +hour's time." Of this continent one of the inquiries was whether +there be a tree in Mexico that yields water, wine, vinegar, milk, +honey, wax, thread and needles. + +Among the problems before the Paris Academy of Sciences those of +physiology and biology took a prominent place. The distillation of +compounds had long been practised, and the fact that the more +spirituous elements of certain substances were thus separated +naturally led to the question whether the essential essences of +life might not be discoverable in the same way. In order that all +might participate in the experiments, they were conducted in open +session of the academy, thus guarding against the danger of any +one member obtaining for his exclusive personal use a possible +elixir of life. A wide range of the animal and vegetable kingdom, +including cats, dogs and birds of various species, were thus +analyzed. The practice of dissection was introduced on a large +scale. That of the cadaver of an elephant occupied several +sessions, and was of such interest that the monarch himself was a +spectator. + +To the same epoch with the formation and first work of these two +bodies belongs the invention of a mathematical method which in its +importance to the advance of exact science may be classed with the +invention of the alphabet in its relation to the progress of +society at large. The use of algebraic symbols to represent +quantities had its origin before the commencement of the new era, +and gradually grew into a highly developed form during the first +two centuries of that era. But this method could represent +quantities only as fixed. It is true that the elasticity inherent +in the use of such symbols permitted of their being applied to any +and every quantity; yet, in any one application, the quantity was +considered as fixed and definite. But most of the magnitudes of +nature are in a state of continual variation; indeed, since all +motion is variation, the latter is a universal characteristic of +all phenomena. No serious advance could be made in the application +of algebraic language to the expression of physical phenomena +until it could be so extended as to express variation in +quantities, as well as the quantities themselves. This extension, +worked out independently by Newton and Leibnitz, may be classed as +the most fruitful of conceptions in exact science. With it the way +was opened for the unimpeded and continually accelerated progress +of the last two centuries. + +The feature of this period which has the closest relation to the +purpose of our coming together is the seemingly unending +subdivision of knowledge into specialties, many of which are +becoming so minute and so isolated that they seem to have no +interest for any but their few pursuers. Happily science itself +has afforded a corrective for its own tendency in this direction. +The careful thinker will see that in these seemingly diverging +branches common elements and common principles are coming more and +more to light. There is an increasing recognition of methods of +research, and of deduction, which are common to large branches, or +to the whole of science. We are more and more recognizing the +principle that progress in knowledge implies its reduction to more +exact forms, and the expression of its ideas in language more or +less mathematical. The problem before the organizers of this +Congress was, therefore, to bring the sciences together, and seek +for the unity which we believe underlies their infinite diversity. + +The assembling of such a body as now fills this hall was scarcely +possible in any preceding generation, and is made possible now +only through the agency of science itself. It differs from all +preceding international meetings by the universality of its scope, +which aims to include the whole of knowledge. It is also unique in +that none but leaders have been sought out as members. It is +unique in that so many lands have delegated their choicest +intellects to carry on its work. They come from the country to +which our republic is indebted for a third of its territory, +including the ground on which we stand; from the land which has +taught us that the most scholarly devotion to the languages and +learning of the cloistered past is compatible with leadership in +the practical application of modern science to the arts of life; +from the island whose language and literature have found a new +field and a vigorous growth in this region; from the last seat of +the holy Roman Empire; from the country which, remembering a +monarch who made an astronomical observation at the Greenwich +Observatory, has enthroned science in one of the highest places in +its government; from the peninsula so learned that we have invited +one of its scholars to come and tells us of our own language; from +the land which gave birth to Leonardo, Galileo, Torricelli, +Columbus, Volta--what an array of immortal names!--from the little +republic of glorious history which, breeding men rugged as its +eternal snow-peaks, has yet been the seat of scientific +investigation since the day of the Bernoullis; from the land whose +heroic dwellers did not hesitate to use the ocean itself to +protect it against invaders, and which now makes us marvel at the +amount of erudition compressed within its little area; from the +nation across the Pacific, which, by half a century of unequalled +progress in the arts of life, has made an important contribution +to evolutionary science through demonstrating the falsity of the +theory that the most ancient races are doomed to be left in the +rear of the advancing age--in a word, from every great centre of +intellectual activity on the globe I see before me eminent +representatives of that world--advance in knowledge which we have +met to celebrate. May we not confidently hope that the discussions +of such an assemblage will prove pregnant of a future for science +which shall outshine even its brilliant past. + +Gentlemen and scholars all! You do not visit our shores to find +great collections in which centuries of humanity have given +expression on canvas and in marble to their hopes, fears, and +aspirations. Nor do you expect institutions and buildings hoary +with age. But as you feel the vigor latent in the fresh air of +these expansive prairies, which has collected the products of +human genius by which we are here surrounded, and, I may add, +brought us together; as you study the institutions which we have +founded for the benefit, not only of our own people, but of +humanity at large; as you meet the men who, in the short space of +one century, have transformed this valley from a savage wilderness +into what it is today--then may you find compensation for the +want of a past like yours by seeing with prophetic eye a future +world-power of which this region shall be the seat. If such is to +be the outcome of the institutions Which we are now building up, +then may your present visit be a blessing both to your posterity +and ours by making that power one for good to all man-kind. Your +deliberations will help to demonstrate to us and to the world at +large that the reign of law must supplant that of brute force in +the relations of the nations, just as it has supplanted it in the +relations of individuals. You will help to show that the war which +science is now waging against the sources of diseases, pain, and +misery offers an even nobler field for the exercise of heroic +qualities than can that of battle. We hope that when, after your +all too-fleeting sojourn in our midst, you return to your own +shores, you will long feel the influence of the new air you have +breathed in an infusion of increased vigor in pursuing your varied +labors. And if a new impetus is thus given to the great +intellectual movement of the past century, resulting not only in +promoting the unification of knowledge, but in widening its field +through new combinations of effort on the part of its votaries, +the projectors, organizers and supporters of this Congress of Arts +and Science will be justified of their labors. + + + + + + +XVII + +THE EVOLUTION OF ASTRONOMICAL KNOWLEDGE + +[Footnote: Address at the dedication of the Flower Observatory, +University of Pennsylvania, May 12, 1897--Science, May 21, 1897] + + +Assembled, as we are, to dedicate a new institution to the +promotion of our knowledge of the heavens, it appeared to me that +an appropriate and interesting subject might be the present and +future problems of astronomy. Yet it seemed, on further +reflection, that, apart from the difficulty of making an adequate +statement of these problems on such an occasion as the present, +such a wording of the theme would not fully express the idea which +I wish to convey. The so-called problems of astronomy are not +separate and independent, but are rather the parts of one great +problem, that of increasing our knowledge of the universe in its +widest extent. Nor is it easy to contemplate the edifice of +astronomical science as it now stands, without thinking of the +past as well as of the present and future. The fact is that our +knowledge of the universe has been in the nature of a slow and +gradual evolution, commencing at a very early period in human +history, and destined to go forward without stop, as we hope, so +long as civilization shall endure. The astronomer of every age has +built on the foundations laid by his predecessors, and his work +has always formed, and must ever form, the base on which his +successors shall build. The astronomer of to-day may look back +upon Hipparchus and Ptolemy as the earliest ancestors of whom he +has positive knowledge. He can trace his scientific descent from +generation to generation, through the periods of Arabian and +medieval science, through Copernicus, Kepler, Newton, Laplace, and +Herschel, down to the present time. The evolution of astronomical +knowledge, generally slow and gradual, offering little to excite +the attention of the public, has yet been marked by two +cataclysms. One of these is seen in the grand conception of +Copernicus that this earth on which we dwell is not a globe fixed +in the centre of the universe, but is simply one of a number of +bodies, turning on their own axes and at the same time moving +around the sun as a centre. It has always seemed to me that the +real significance of the heliocentric system lies in the greatness +of this conception rather than in the fact of the discovery +itself. There is no figure in astronomical history which may more +appropriately claim the admiration of mankind through all time +than that of Copernicus. Scarcely any great work was ever so +exclusively the work of one man as was the heliocentric system the +work of the retiring sage of Frauenburg. No more striking contrast +between the views of scientific research entertained in his time +and in ours can be found than that afforded by the fact that, +instead of claiming credit for his great work, he deemed it rather +necessary to apologize for it and, so far as possible, to +attribute his ideas to the ancients. + +A century and a half after Copernicus followed the second great +step, that taken by Newton. This was nothing less than showing +that the seemingly complicated and inexplicable motions of the +heavenly bodies were only special cases of the same kind of +motion, governed by the same forces, that we see around us +whenever a stone is thrown by the hand or an apple falls to the +ground. The actual motions of the heavens and the laws which +govern them being known, man had the key with which he might +commence to unlock the mysteries of the universe. + +When Huyghens, in 1656, published his Systema Saturnium, where he +first set forth the mystery of the rings of Saturn, which, for +nearly half a century, had perplexed telescopic observers, he +prefaced it with a remark that many, even among the learned, might +condemn his course in devoting so much time and attention to +matters far outside the earth, when he might better be studying +subjects of more concern to humanity. Notwithstanding that the +inventor of the pendulum clock was, perhaps, the last astronomer +against whom a neglect of things terrestrial could be charged, he +thought it necessary to enter into an elaborate defence of his +course in studying the heavens. Now, however, the more distant +objects are in space--I might almost add the more distant events +are in time--the more they excite the attention of the astronomer, +if only he can hope to acquire positive knowledge about them. Not, +however, because he is more interested in things distant than in +things near, but because thus he may more completely embrace in +the scope of his work the beginning and the end, the boundaries of +all things, and thus, indirectly, more fully comprehend all that +they include. From his stand-point, + + "All are but parts of one stupendous whole, + Whose body Nature is and God the soul." + +Others study Nature and her plans as we see them developed on the +surface of this little planet which we inhabit, the astronomer +would fain learn the plan on which the whole universe is +constructed. The magnificent conception of Copernicus is, for him, +only an introduction to the yet more magnificent conception of +infinite space containing a collection of bodies which we call the +visible universe. How far does this universe extend? What are the +distances and arrangements of the stars? Does the universe +constitute a system? If so, can we comprehend the plan on which +this system is formed, of its beginning and of its end? Has it +bounds outside of which nothing exists but the black and starless +depths of infinity itself? Or are the stars we see simply such +members of an infinite collection as happen to be the nearest our +system? A few such questions as these we are perhaps beginning to +answer; but hundreds, thousands, perhaps even millions, of years +may elapse without our reaching a complete solution. Yet the +astronomer does not view them as Kantian antinomies, in the nature +of things insoluble, but as questions to which he may hopefully +look for at least a partial answer. + +The problem of the distances of the stars is of peculiar interest +in connection with the Copernican system. The greatest objection +to this system, which must have been more clearly seen by +astronomers themselves than by any others, was found in the +absence of any apparent parallax of the stars. If the earth +performed such an immeasurable circle around the sun as Copernicus +maintained, then, as it passed from side to side of its orbit, the +stars outside the solar system must appear to have a corresponding +motion in the other direction, and thus to swing back and forth as +the earth moved in one and the other direction. The fact that not +the slightest swing of that sort could be seen was, from the time +of Ptolemy, the basis on which the doctrine of the earth's +immobility rested. The difficulty was not grappled with by +Copernicus or his immediate successors. The idea that Nature would +not squander space by allowing immeasurable stretches of it to go +unused seems to have been one from which medieval thinkers could +not entirely break away. The consideration that there could be no +need of any such economy, because the supply was infinite, might +have been theoretically acknowledged, but was not practically +felt. The fact is that magnificent as was the conception of +Copernicus, it was dwarfed by the conception of stretches from +star to star so vast that the whole orbit of the earth was only a +point in comparison. + +An indication of the extent to which the difficulty thus arising +was felt is seen in the title of a book published by Horrebow, the +Danish astronomer, some two centuries ago. This industrious +observer, one of the first who used an instrument resembling our +meridian transit of the present day, determined to see if he could +find the parallax of the stars by observing the intervals at which +a pair of stars in opposite quarters of the heavens crossed his +meridian at opposite seasons of the year. When, as he thought, he +had won success, he published his observations and conclusions +under the title of Copernicus Triumphans. But alas! the keen +criticism of his successors showed that what he supposed to be a +swing of the stars from season to season arose from a minute +variation in the rate of his clock, due to the different +temperatures to which it was exposed during the day and the night. +The measurement of the distance even of the nearest stars evaded +astronomical research until Bessel and Struve arose in the early +part of the present century. + +On some aspects of the problem of the extent of the universe light +is being thrown even now. Evidence is gradually accumulating which +points to the probability that the successive orders of smaller +and smaller stars, which our continually increasing telescopic +power brings into view, are not situated at greater and greater +distances, but that we actually see the boundary of our universe. +This indication lends a peculiar interest to various questions +growing out of the motions of the stars. Quite possibly the +problem of these motions will be the great one of the future +astronomer. Even now it suggests thoughts and questions of the +most far-reaching character. + +I have seldom felt a more delicious sense of repose than when +crossing the ocean during the summer months I sought a place where +I could lie alone on the deck, look up at the constellations, with +Lyra near the zenith, and, while listening to the clank of the +engine, try to calculate the hundreds of millions of years which +would be required by our ship to reach the star a Lyrae, if she +could continue her course in that direction without ever stopping. +It is a striking example of how easily we may fail to realize our +knowledge when I say that I have thought many a time how +deliciously one might pass those hundred millions of years in a +journey to the star a Lyrae, without its occurring to me that we +are actually making that very journey at a speed compared with +which the motion of a steamship is slow indeed. Through every +year, every hour, every minute, of human history from the first +appearance of man on the earth, from the era of the builders of +the Pyramids, through the times of Caesar and Hannibal, through +the period of every event that history records, not merely our +earth, but the sun and the whole solar system with it, have been +speeding their way towards the star of which I speak on a journey +of which we know neither the beginning nor the end. We are at this +moment thousands of miles nearer to a Lyrae than we were a few +minutes ago when I began this discourse, and through every future +moment, for untold thousands of years to come, the earth and all +there is on it will be nearer to a Lyrae, or nearer to the place +where that star now is, by hundreds of miles for every minute of +time come and gone. When shall we get there? Probably in less than +a million years, perhaps in half a million. We cannot tell +exactly, but get there we must if the laws of nature and the laws +of motion continue as they are. To attain to the stars was the +seemingly vain wish of an ancient philosopher, but the whole human +race is, in a certain sense, realizing this wish as rapidly as a +speed of ten miles a second can bring it about. + +I have called attention to this motion because it may, in the not +distant future, afford the means of approximating to a solution of +the problem already mentioned--that of the extent of the universe. +Notwithstanding the success of astronomers during the present +century in measuring the parallax of a number of stars, the most +recent investigations show that there are very few, perhaps hardly +more than a score, of stars of which the parallax, and therefore +the distance, has been determined with any approach to certainty. +Many parallaxes determined about the middle of the nineteenth +century have had to disappear before the powerful tests applied by +measures with the heliometer; others have been greatly reduced and +the distances of the stars increased in proportion. So far as +measurement goes, we can only say of the distances of all the +stars, except the few whose parallaxes have been determined, that +they are immeasurable. The radius of the earth's orbit, a line +more than ninety millions of miles in length, not only vanishes +from sight before we reach the distance of the great mass of +stars, but becomes such a mere point that when magnified by the +powerful instruments of modern times the most delicate appliances +fail to make it measurable. Here the solar motion comes to our +help. This motion, by which, as I have said, we are carried +unceasingly through space, is made evident by a motion of most of +the stars in the opposite direction, just as passing through a +country on a railway we see the houses on the right and on the +left being left behind us. It is clear enough that the apparent +motion will be more rapid the nearer the object. We may therefore +form some idea of the distance of the stars when we know the +amount of the motion. It is found that in the great mass of stars +of the sixth magnitude, the smallest visible to the naked eye, the +motion is about three seconds per century. As a measure thus +stated does not convey an accurate conception of magnitude to one +not practised in the subject, I would say that in the heavens, to +the ordinary eye, a pair of stars will appear single unless they +are separated by a distance of 150 or 200 seconds. Let us, then, +imagine ourselves looking at a star of the sixth magnitude, which +is at rest while we are carried past it with the motion of six to +eight miles per second which I have described. Mark its position +in the heavens as we see it to-day; then let its position again be +marked five thousand years hence. A good eye will just be able to +perceive that there are two stars marked instead of one. The two +would be so close together that no distinct space between them +could be perceived by unaided vision. It is due to the magnifying +power of the telescope, enlarging such small apparent distances, +that the motion has been determined in so small a period as the +one hundred and fifty years during which accurate observations of +the stars have been made. + +The motion just described has been fairly well determined for +what, astronomically speaking, are the brighter stars; that is to +say, those visible to the naked eye. But how is it with the +millions of faint telescopic stars, especially those which form +the cloud masses of the Milky Way? The distance of these stars is +undoubtedly greater, and the apparent motion is therefore smaller. +Accurate observations upon such stars have been commenced only +recently, so that we have not yet had time to determine the amount +of the motion. But the indication seems to be that it will prove +quite a measurable quantity and that before the twentieth century +has elapsed, it will be determined for very much smaller stars +than those which have heretofore been studied. A photographic +chart of the whole heavens is now being constructed by an +association of observatories in some of the leading countries of +the world. I cannot say all the leading countries, because then we +should have to exclude our own, which, unhappily, has taken no +part in this work. At the end of the twentieth century we may +expect that the work will be repeated. Then, by comparing the +charts, we shall see the effect of the solar motion and perhaps +get new light upon the problem in question. + +Closely connected with the problem of the extent of the universe +is another which appears, for us, to be insoluble because it +brings us face to face with infinity itself. We are familiar +enough with eternity, or, let us say, the millions or hundreds of +millions of years which geologists tell us must have passed while +the crust of the earth was assuming its present form, our +mountains being built, our rocks consolidated, and successive +orders of animals coming and going. Hundreds of millions of years +is indeed a long time, and yet, when we contemplate the changes +supposed to have taken place during that time, we do not look out +on eternity itself, which is veiled from our sight, as it were, by +the unending succession of changes that mark the progress of time. +But in the motions of the stars we are brought face to face with +eternity and infinity, covered by no veil whatever. It would be +bold to speak dogmatically on a subject where the springs of being +are so far hidden from mortal eyes as in the depths of the +universe. But, without declaring its positive certainty, it must +be said that the conclusion seems unavoidable that a number of +stars are moving with a speed such that the attraction of all the +bodies of the universe could never stop them. One such case is +that of Arcturus, the bright reddish star familiar to mankind +since the days of Job, and visible near the zenith on the clear +evenings of May and June. Yet another case is that of a star known +in astronomical nomenclature as 1830 Groombridge, which exceeds +all others in its angular proper motion as seen from the earth. We +should naturally suppose that it seems to move so fast because it +is near us. But the best measurements of its parallax seem to show +that it can scarcely be less than two million times the distance +of the earth from the sun, while it may be much greater. Accepting +this result, its velocity cannot be much less than two hundred +miles per second, and may be much more. With this speed it would +make the circuit of our globe in two minutes, and had it gone +round and round in our latitudes we should have seen it fly past +us a number of times since I commenced this discourse. It would +make the journey from the earth to the sun in five days. If it is +now near the centre of our universe it would probably reach its +confines in a million of years. So far as our knowledge goes, +there is no force in nature which would ever have set it in motion +and no force which can ever stop it. What, then, was the history +of this star, and, if there are planets circulating around, what +the experience of beings who may have lived on those planets +during the ages which geologists and naturalists assure us our +earth has existed? Was there a period when they saw at night only +a black and starless heaven? Was there a time when in that heaven +a small faint patch of light began gradually to appear? Did that +patch of light grow larger and larger as million after million of +years elapsed? Did it at last fill the heavens and break up into +constellations as we now see them? As millions more of years +elapse will the constellations gather together in the opposite +quarter and gradually diminish to a patch of light as the star +pursues its irresistible course of two hundred miles per second +through the wilderness of space, leaving our universe farther and +farther behind it, until it is lost in the distance? If the +conceptions of modern science are to be considered as good for all +time--a point on which I confess to a large measure of scepticism-- +then these questions must be answered in the affirmative. + +The problems of which I have so far spoken are those of what may +be called the older astronomy. If I apply this title it is because +that branch of the science to which the spectroscope has given +birth is often called the new astronomy. It is commonly to be +expected that a new and vigorous form of scientific research will +supersede that which is hoary with antiquity. But I am not willing +to admit that such is the case with the old astronomy, if old we +may call it. It is more pregnant with future discoveries today +than it ever has been, and it is more disposed to welcome the +spectroscope as a useful handmaid, which may help it on to new +fields, than it is to give way to it. How useful it may thus +become has been recently shown by a Dutch astronomer, who finds +that the stars having one type of spectrum belong mostly to the +Milky Way, and are farther from us than the others. + +In the field of the newer astronomy perhaps the most interesting +work is that associated with comets. It must be confessed, +however, that the spectroscope has rather increased than +diminished the mystery which, in some respects, surrounds the +constitution of these bodies. The older astronomy has +satisfactorily accounted for their appearance, and we might also +say for their origin and their end, so far as questions of origin +can come into the domain of science. It is now known that comets +are not wanderers through the celestial spaces from star to star, +but must always have belonged to our system. But their orbits are +so very elongated that thousands, or even hundreds of thousands, +of years are required for a revolution. Sometimes, however, a +comet passing near to Jupiter is so fascinated by that planet +that, in its vain attempts to follow it, it loses so much of its +primitive velocity as to circulate around the sun in a period of a +few years, and thus to become, apparently, a new member of our +system. If the orbit of such a comet, or in fact of any comet, +chances to intersect that of the earth, the latter in passing the +point of intersection encounters minute particles which cause a +meteoric shower. + +But all this does not tell us much about the nature and make-up of +a comet. Does it consist of nothing but isolated particles, or is +there a solid nucleus, the attraction of which tends to keep the +mass together? No one yet knows. The spectroscope, if we interpret +its indications in the usual way, tells us that a comet is simply +a mass of hydrocarbon vapor, shining by its own light. But there +must be something wrong in this interpretation. That the light is +reflected sunlight seems to follow necessarily from the increased +brilliancy of the comet as it approaches the sun and its +disappearance as it passes away. + +Great attention has recently been bestowed upon the physical +constitution of the planets and the changes which the surfaces of +those bodies may undergo. In this department of research we must +feel gratified by the energy of our countrymen who have entered +upon it. Should I seek to even mention all the results thus made +known I might be stepping on dangerous ground, as many questions +are still unsettled. While every astronomer has entertained the +highest admiration for the energy and enthusiasm shown by Mr. +Percival Lowell in founding an observatory in regions where the +planets can be studied under the most favorable conditions, they +cannot lose sight of the fact that the ablest and most experienced +observers are liable to error when they attempt to delineate the +features of a body 50,000,000 or 100,000,000 miles away through +such a disturbing medium as our atmosphere. Even on such a subject +as the canals of Mars doubts may still be felt. That certain +markings to which Schiaparelli gave the name of canals exist, few +will question. But it may be questioned whether these markings are +the fine, sharp, uniform lines found on Schiaparelli's map and +delineated in Lowell's beautiful book. It is certainly curious +that Barnard at Mount Hamilton, with the most powerful instrument +and under the most favorable circumstances, does not see these +markings as canals. + +I can only mention among the problems of the spectroscope the +elegant and remarkable solution of the mystery surrounding the +rings of Saturn, which has been effected by Keeler at Allegheny. +That these rings could not be solid has long been a conclusion of +the laws of mechanics, but Keeler was the first to show that they +really consist of separate particles, because the inner portions +revolve more rapidly than the outer. + +The question of the atmosphere of Mars has also received an +important advance by the work of Campbell at Mount Hamilton. +Although it is not proved that Mars has no atmosphere, for the +existence of some atmosphere can scarcely be doubted, yet the +Mount Hamilton astronomer seems to have shown, with great +conclusiveness, that it is so rare as not to produce any sensible +absorption of the solar rays. + +I have left an important subject for the close. It belongs +entirely to the older astronomy, and it is one with which I am +glad to say this observatory is expected to especially concern +itself. I refer to the question of the variation of latitudes, +that singular phenomenon scarcely suspected ten years ago, but +brought out by observations in Germany during the past eight +years, and reduced to law with such brilliant success by our own +Chandler. The north pole is not a fixed point on the earth's +surface, but moves around in rather an irregular way. True, the +motion is small; a circle of sixty feet in diameter will include +the pole in its widest range. This is a very small matter so far +as the interests of daily life are concerned; but it is very +important to the astronomer. It is not simply a motion of the pole +of the earth, but a wobbling of the solid earth itself. No one +knows what conclusions of importance to our race may yet follow +from a study of the stupendous forces necessary to produce even +this slight motion. + +The director of this new observatory has already distinguished +himself in the delicate and difficult work of investigating this +motion, and I am glad to know that he is continuing the work here +with one of the finest instruments ever used for the purpose, a +splendid product of American mechanical genius. I can assure you +that astronomers the world over will look with the greatest +interest for Professor Doolittle's success in the arduous task he +has undertaken. + +There is one question connected with these studies of the universe +on which I have not touched, and which is, nevertheless, of +transcendent interest. What sort of life, spiritual and +intellectual, exists in distant worlds? We cannot for a moment +suppose that our little planet is the only one throughout the +whole universe on which may be found the fruits of civilization, +family affection, friendship, the desire to penetrate the +mysteries of creation. And yet this question is not to-day a +problem of astronomy, nor can we see any prospect that it ever +will be, for the simple reason that science affords us no hope of +an answer to any question that we may send through the fathomless +abyss. When the spectroscope was in its infancy it was suggested +that possibly some difference might be found in the rays reflected +from living matter, especially from vegetation, that might enable +us to distinguish them from rays reflected by matter not endowed +with life. But this hope has not been realized, nor does it seem +possible to realize it. The astronomer cannot afford to waste his +energies on hopeless speculation about matters of which he cannot +learn anything, and he therefore leaves this question of the +plurality of worlds to others who are as competent to discuss it +as he is. All he can tell the world is: + + He who through vast immensity can pierce, + See worlds on worlds compose one universe; + Observe how system into system runs, + What other planets circle other suns, + What varied being peoples every star, + May tell why Heaven has made us as we are. + + + + + +XVIII + +ASPECTS OF AMERICAN ASTRONOMY + +[Footnote: Address delivered at the University of Chicago, October +22, 1897, in connection with the dedication of the Yerkes +Observatory. Printed m the Astro physical Journal. November, 1897.] + + +The University of Chicago yesterday accepted one of the most +munificent gifts ever made for the promotion of any single +science, and with appropriate ceremonies dedicated it to the +increase of our knowledge of the heavenly bodies. + +The president of your university has done me the honor of inviting +me to supplement what was said on that occasion by some remarks of +a more general nature suggested by the celebration. One is +naturally disposed to say first what is uppermost in his mind. At +the present moment this will naturally be the general impression +made by what has been seen and heard. The ceremonies were +attended, not only by a remarkable delegation of citizens, but by +a number of visiting astronomers which seems large when we +consider that the profession itself is not at all numerous in any +country. As one of these, your guests, I am sure that I give +expression only to their unanimous sentiment in saying that we +have been extremely gratified in many ways by all that we have +seen and heard. The mere fact of so munificent a gift to science +cannot but excite universal admiration. We knew well enough that +it was nothing more than might have been expected from the public +spirit of this great West; but the first view of a towering +snowpeak is none the less impressive because you have learned in +your geography how many feet high it is, and great acts are none +the less admirable because they correspond to what you have heard +and read, and might therefore be led to expect. + +The next gratifying feature is the great public interest excited +by the occasion. That the opening of a purely scientific +institution should have led so large an assemblage of citizens to +devote an entire day, including a long journey by rail, to the +celebration of yesterday is something most suggestive from its +unfamiliarity. A great many scientific establishments have been +inaugurated during the last half-century, but if on any such +occasion so large a body of citizens has gone so great a distance +to take part in the inauguration, the fact has at the moment +escaped my mind. + +That the interest thus shown is not confined to the hundreds of +attendants, but must be shared by your great public, is shown by +the unfailing barometer of journalism. Here we have a field in +which the non-survival of the unfit is the rule in its most +ruthless form. The journals that we see and read are merely the +fortunate few of a countless number, dead and forgotten, that did +not know what the public wanted to read about. The eagerness shown +by the representatives of your press in recording everything your +guests would say was accomplished by an enterprise in making known +everything that occurred, and, in case of an emergency requiring a +heroic measure, what did NOT occur, showing that smart journalists +of the East must have learned their trade, or at least breathed +their inspiration, in these regions. I think it was some twenty +years since I told a European friend that the eighth wonder of the +world was a Chicago daily newspaper. Since that time the course of +journalistic enterprise has been in the reverse direction to that +of the course of empire, eastward instead of westward. + +It has been sometimes said--wrongfully, I think--that scientific +men form a mutual admiration society. One feature of the occasion +made me feel that we, your guests, ought then and there to have +organized such a society and forthwith proceeded to business. This +feature consisted in the conferences on almost every branch of +astronomy by which the celebration of yesterday was preceded. The +fact that beyond the acceptance of a graceful compliment I +contributed nothing to these conferences relieves me from the +charge of bias or self-assertion in saying that they gave me a new +and most inspiring view of the energy now being expended in +research by the younger generation of astronomers. All the +experience of the past leads us to believe that this energy will +reap the reward which nature always bestows upon those who seek +her acquaintance from unselfish motives. In one way it might +appear that little was to be learned from a meeting like that of +the present week. Each astronomer may know by publications +pertaining to the science what all the others are doing. But +knowledge obtained in this way has a sort of abstractness about it +a little like our knowledge of the progress of civilization in +Japan, or of the great extent of the Australian continent. It was, +therefore, a most happy thought on the part of your authorities to +bring together the largest possible number of visiting astronomers +from Europe, as well as America, in order that each might see, +through the attrition of personal contact, what progress the +others were making in their researches. To the visitors at least I +am sure that the result of this meeting has been extremely +gratifying. They earnestly hope, one and all, that the callers of +the conference will not themselves be more disappointed in its +results; that, however little they may have actually to learn of +methods and results, they will feel stimulated to well-directed +efforts and find themselves inspired by thoughts which, however +familiar, will now be more easily worked out. + +We may pass from the aspects of the case as seen by the strictly +professional class to those general aspects fitted to excite the +attention of the great public. From the point of view of the +latter it may well appear that the most striking feature of the +celebration is the great amount of effort which is shown to be +devoted to the cultivation of a field quite outside the ordinary +range of human interests. The workers whom we see around us are +only a detachment from an army of investigators who, in many parts +of the world, are seeking to explore the mysteries of creation. +Why so great an expenditure of energy? Certainly not to gain +wealth, for astronomy is perhaps the one field of scientific work +which, in our expressive modern phrase, "has no money in it." It +is true that the great practical use of astronomical science to +the country and the world in affording us the means of determining +positions on land and at sea is frequently pointed out. It is said +that an Astronomer Royal of England once calculated that every +meridian observation of the moon made at Greenwich was worth a +pound sterling, on account of the help it would afford to the +navigation of the ocean. An accurate map of the United States +cannot be constructed without astronomical observations at +numerous points scattered over the whole country, aided by data +which great observatories have been accumulating for more than a +century, and must continue to accumulate in the future. + +But neither the measurement of the earth, the making of maps, nor +the aid of the navigator is the main object which the astronomers +of to-day have in view. If they do not quite share the sentiment +of that eminent mathematician, who is said to have thanked God +that his science was one which could not be prostituted to any +useful purpose, they still know well that to keep utilitarian +objects in view would only prove & handicap on their efforts. +Consequently they never ask in what way their science is going to +benefit mankind. As the great captain of industry is moved by the +love of wealth, and the political leader by the love of power over +men, so the astronomer is moved by the love of knowledge for its +own sake, and not for the sake of its useful applications. Yet he +is proud to know that his science has been worth more to mankind +than it has cost. He does not value its results merely as a means +of crossing the ocean or mapping the country, for he feels that +man does not live by bread alone. If it is not more than bread to +know the place we occupy in the universe, it is certainly +something which we should place not far behind the means of +subsistence. That we now look upon a comet as something very +interesting, of which the sight affords us a pleasure unmixed with +fear of war, pestilence, or other calamity, and of which we +therefore wish the return, is a gain we cannot measure by money. +In all ages astronomy has been an index to the civilization of the +people who cultivated it. It has been crude or exact, enlightened +or mingled with superstition, according to the current mode of +thought. When once men understand the relation of the planet on +which they dwell to the universe at large, superstition is doomed +to speedy extinction. This alone is an object worth more than +money. + +Astronomy may fairly claim to be that science which transcends all +others in its demands upon the practical application of our +reasoning powers. Look at the stars that stud the heavens on a +clear evening. What more hopeless problem to one confined to earth +than that of determining their varying distances, their motions, +and their physical constitution? Everything on earth we can handle +and investigate. But how investigate that which is ever beyond our +reach, on which we can never make an experiment? On certain +occasions we see the moon pass in front of the sun and hide it +from our eyes. To an observer a few miles away the sun was not +entirely hidden, for the shadow of the moon in a total eclipse is +rarely one hundred miles wide. On another continent no eclipse at +all may have been visible. Who shall take a map of the world and +mark upon it the line on which the moon's shadow will travel +during some eclipse a hundred years hence? Who shall map out the +orbits of the heavenly bodies as they are going to appear in a +hundred thousand years? How shall we ever know of what chemical +elements the sun and the stars are made? All this has been done, +but not by the intellect of any one man. The road to the stars has +been opened only by the efforts of many generations of +mathematicians and observers, each of whom began where his +predecessor had left off. + +We have reached a stage where we know much of the heavenly +bodies. We have mapped out our solar system with great precision. +But how with that great universe of millions of stars in which our +solar system is only a speck of star-dust, a speck which a +traveller through the wilds of space might pass a hundred times +without notice? We have learned much about this universe, though +our knowledge of it is still dim. We see it as a traveller on a +mountain-top sees a distant city in a cloud of mist, by a few +specks of glimmering light from steeples or roofs. We want to know +more about it, its origin and its destiny; its limits in time and +space, if it has any; what function it serves in the universal +economy. The journey is long, yet we want, in knowledge at least, +to make it. Hence we build observatories and train observers and +investigators. Slow, indeed, is progress in the solution of the +greatest of problems, when measured by what we want to know. Some +questions may require centuries, others thousands of years for +their answer. And yet never was progress more rapid than during +our time. In some directions our astronomers of to-day are out of +sight of those of fifty years ago; we are even gaining heights +which twenty years ago looked hopeless. Never before had the +astronomer so much work--good, hard, yet hopeful work--before him +as to-day. He who is leaving the stage feels that he has only +begun and must leave his successors with more to do than his +predecessors left him. + +To us an interesting feature of this progress is the part taken in +it by our own country. The science of our day, it is true, is of +no country. Yet we very appropriately speak of American science +from the fact that our traditional reputation has not been that of +a people deeply interested in the higher branches of intellectual +work. Men yet living can remember when in the eyes of the +universal church of learning, all cisatlantic countries, our own +included, were partes infidelium. + +Yet American astronomy is not entirely of our generation. In the +middle of the last century Professor Winthrop, of Harvard, was an +industrious observer of eclipses and kindred phenomena, whose work +was recorded in the transactions of learned societies. But the +greatest astronomical activity during our colonial period was that +called out by the transit of Venus in 1769, which was visible in +this country. A committee of the American Philosophical Society, +at Philadelphia, organized an excellent system of observations, +which we now know to have been fully as successful, perhaps more +so, than the majority of those made on other continents, owing +mainly to the advantages of air and climate. Among the observers +was the celebrated Rittenhouse, to whom is due the distinction of +having been the first American astronomer whose work has an +important place in the history of the science. In addition to the +observations which he has left us, he was the first inventor or +proposer of the collimating telescope, an instrument which has +become almost a necessity wherever accurate observations are made. +The fact that the subsequent invention by Bessel may have been +independent does not detract from the merits of either. + +Shortly after the transit of Venus, which I have mentioned, the +war of the Revolution commenced. The generation which carried on +that war and the following one, which framed our Constitution and +laid the bases of our political institutions, were naturally too +much occupied with these great problems to pay much attention to +pure science. While the great mathematical astronomers of Europe +were laying the foundation of celestial mechanics their writings +were a sealed book to every one on this side of the Atlantic, and +so remained until Bowditch appeared, early in the present century. +His translation of the Mecanique Celeste made an epoch in American +science by bringing the great work of Laplace down to the reach of +the best American students of his time. + +American astronomers must always honor the names of Rittenhouse +and Bowditch. And yet in one respect their work was disappointing +of results. Neither of them was the founder of a school. Rittenhouse +left no successor to carry on his work. The help which +Bowditch afforded his generation was invaluable to isolated +students who, here and there, dived alone and unaided into the +mysteries of the celestial motions. His work was not mainly in the +field of observational astronomy, and therefore did not materially +influence that branch of science. In 1832 Professor Airy, +afterwards Astronomer Royal of England, made a report to the +British Association on the condition of practical astronomy in +various countries. In this report he remarked that he was unable +to say anything about American astronomy because, so far as he +knew, no public observatory existed in the United States. + +William C. Bond, afterwards famous as the first director of the +Harvard Observatory, was at that time making observations with a +small telescope, first near Boston and afterwards at Cambridge. +But with so meagre an outfit his establishment could scarcely lay +claim to being an astronomical observatory, and it was not +surprising if Airy did not know anything of his modest efforts. + +If at this time Professor Airy had extended his investigations +into yet another field, with a view of determining the prospects +for a great city at the site of Fort Dearborn, on the southern +shore of Lake Michigan, he would have seen as little prospect of +civic growth in that region as of a great development of astronomy +in the United States at large. A plat of the proposed town of +Chicago had been prepared two years before, when the place +contained perhaps half a dozen families. In the same month in +which Professor Airy made his report, August, 1832, the people of +the place, then numbering twenty-eight voters, decided to become +incorporated, and selected five trustees to carry on their +government. + +In 1837 a city charter was obtained from the legislature of +Illinois. The growth of this infant city, then small even for an +infant, into the great commercial metropolis of the West has been +the just pride of its people and the wonder of the world. I +mention it now because of a remarkable coincidence. With this +civic growth has quietly gone on another, little noted by the +great world, and yet in its way equally wonderful and equally +gratifying to the pride of those who measure greatness by +intellectual progress. Taking knowledge of the universe as a +measure of progress, I wish to invite attention to the fact that +American astronomy began with your city, and has slowly but surely +kept pace with it, until to-day our country stands second only to +Germany in the number of researches being prosecuted, and second +to none in the number of men who have gained the highest +recognition by their labors. + +In 1836 Professor Albert Hopkins, of Williams College, and +Professor Elias Loomis, of Western Reserve College, Ohio, both +commenced little observatories. Professor Loomis went to Europe +for all his instruments, but Hopkins was able even then to get +some of his in this country. Shortly afterwards a little wooden +structure was erected by Captain Gilliss on Capitol Hill, at +Washington, and supplied with a transit instrument for observing +moon culminations, in conjunction with Captain Wilkes, who was +then setting out on his exploring expedition to the southern +hemisphere. The date of these observatories was practically the +same as that on which a charter for the city of Chicago was +obtained from the legislature. With their establishment the +population of your city had increased to 703. + +The next decade, 1840 to 1850, was that in which our practical +astronomy seriously commenced. The little observatory of Captain +Gilliss was replaced by the Naval, then called the National +Observatory, erected at Washington during the years 1843-44, and +fitted out with what were then the most approved instruments. +About the same time the appearance of the great comet of 1843 led +the citizens of Boston to erect the observatory of Harvard +College. Thus it is little more than a half-century since the two +principal observatories in the United States were established. But +we must not for a moment suppose that the mere erection of an +observatory can mark an epoch in scientific history. What must +make the decade of which I speak ever memorable in American +astronomy was not merely the erection of buildings, but the +character of the work done by astronomers away from them as well +as in them. + +The National Observatory soon became famous by two remarkable +steps which raised our country to an important position among +those applying modern science to practical uses. One of these +consisted of the researches of Sears Cook Walker on the motion of +the newly discovered planet Neptune. He was the first astronomer +to determine fairly good elements of the orbit of that planet, +and, what is yet more remarkable, he was able to trace back the +movement of the planet in the heavens for half a century and to +show that it had been observed as a fixed star by Lalande in 1795, +without the observer having any suspicion of the true character of +the object. + +The other work to which I refer was the application to astronomy +and to the determination of longitudes of the chronographic method +of registering transits of stars or other phenomena requiring an +exact record of the instant of their occurrence. It is to be +regretted that the history of this application has not been fully +written. In some points there seems to be as much obscurity as +with the discovery of ether as an anaesthetic, which took place +about the same time. Happily, no such contest has been fought over +the astronomical as over the surgical discovery, the fact being +that all who were engaged in the application of the new method +were more anxious to perfect it than they were to get credit for +themselves. We know that Saxton, of the Coast Survey; Mitchell and +Locke, of Cincinnati; Bond, at Cambridge, as well as Walker, and +other astronomers at the Naval Observatory, all worked at the +apparatus; that Maury seconded their efforts with untiring zeal; +that it was used to determine the longitude of Baltimore as early +as 1844 by Captain Wilkes, and that it was put into practical use +in recording observations at the Naval Observatory as early as +1846. + +At the Cambridge Observatory the two Bonds, father and son, +speedily began to show the stuff of which the astronomer is made. +A well-devised system of observations was put in operation. The +discovery of the dark ring of Saturn and of a new satellite to +that planet gave additional fame to the establishment. + +Nor was activity confined to the observational side of the +science. The same decade of which I speak was marked by the +beginning of Professor Pierce's mathematical work, especially his +determination of the perturbations of Uranus and Neptune. At this +time commenced the work of Dr. B. A. Gould, who soon became the +leading figure in American astronomy. Immediately on graduating at +Harvard in 1845, he determined to devote all the energies of his +life to the prosecution of his favorite science. He studied in +Europe for three years, took the doctor's degree at Gottingen, +came home, founded the Astronomical Journal, and took an active +part in that branch of the work of the Coast Survey which included +the determination of longitudes by astronomical methods. + +An episode which may not belong to the history of astronomy must +be acknowledged to have had a powerful influence in exciting +public interest in that science. Professor O. M. Mitchell, the +founder and first director of the Cincinnati Observatory, made the +masses of our intelligent people acquainted with the leading facts +of astronomy by courses of lectures which, in lucidity and +eloquence, have never been excelled. The immediate object of the +lectures was to raise funds for establishing his observatory and +fitting it out with a fine telescope. The popular interest thus +excited in the science had an important effect in leading the +public to support astronomical research. If public support, based +on public interest, is what has made the present fabric of +American astronomy possible, then should we honor the name of a +man whose enthusiasm leavened the masses of his countrymen with +interest in our science. + +The Civil War naturally exerted a depressing influence upon our +scientific activity. The cultivator of knowledge is no less +patriotic than his fellow-citizens, and vies with them in devotion +to the public welfare. The active interest which such cultivators +took, first in the prosecution of the war and then in the +restoration of the Union, naturally distracted their attention +from their favorite pursuits. But no sooner was political +stability reached than a wave of intellectual activity set in, +which has gone on increasing up to the present time. If it be true +that never before in our history has so much attention been given +to education as now; that never before did so many men devote +themselves to the diffusion of knowledge, it is no less true that +never was astronomical work so energetically pursued among us as +at the present time. + +One deplorable result of the Civil War was that Gould's +Astronomical Journal had to be suspended. Shortly after the +restoration of peace, instead of re-establishing the journal, its +founder conceived the project of exploring the southern heavens. +The northern hemisphere being the seat of civilization, that +portion of the sky which could not be seen from our latitudes was +comparatively neglected. What had been done in the southern +hemisphere was mostly the occasional work of individuals and of +one or two permanent observatories. The latter were so few in +number and so meagre in their outfit that a splendid field was +open to the inquirer. Gould found the patron which he desired in +the government of the Argentine Republic, on whose territory he +erected what must rank in the future as one of the memorable +astronomical establishments of the world. His work affords a most +striking example of the principle that the astronomer is more +important than his instruments. Not only were the means at the +command of the Argentine Observatory slender in the extreme when +compared with those of the favored institutions of the North, but, +from the very nature of the case, the Argentine Republic could not +supply trained astronomers. The difficulties thus growing out of +the administration cannot be overestimated. And yet the sixteen +great volumes in which the work of the institution has been +published will rank in the future among the classics of astronomy. + +Another wonderful focus of activity, in which one hardly knows +whether he ought most to admire the exhaustless energy or the +admirable ingenuity which he finds displayed, is the Harvard +Observatory. Its work has been aided by gifts which have no +parallel in the liberality that prompted them. Yet without energy +and skill such gifts would have been useless. The activity of the +establishment includes both hemispheres. Time would fail to tell +how it has not only mapped out important regions of the heavens +from the north to the south pole, but analyzed the rays of light +which come from hundreds of thousands of stars by recording their +spectra in permanence on photographic plates. + +The work of the establishment is so organized that a new star +cannot appear in any part of the heavens nor a known star undergo +any noteworthy change without immediate detection by the +photographic eye of one or more little telescopes, all-seeing and +never-sleeping policemen that scan the heavens unceasingly while +the astronomer may sleep, and report in the morning every case of +irregularity in the proceedings of the heavenly bodies. + +Yet another example, showing what great results may be obtained +with limited means, is afforded by the Lick Observatory, on Mount +Hamilton, California. During the ten years of its activity its +astronomers have made it known the world over by works and +discoveries too varied and numerous to be even mentioned at the +present time. + +The astronomical work of which I have thus far spoken has been +almost entirely that done at observatories. I fear that I may in +this way have strengthened an erroneous impression that the seat +of important astronomical work is necessarily connected with an +observatory. It must be admitted that an institution which has a +local habitation and a magnificent building commands public +attention so strongly that valuable work done elsewhere may be +overlooked. A very important part of astronomical work is done +away from telescopes and meridian circles and requires nothing but +a good library for its prosecution. One who is devoted to this +side of the subject may often feel that the public does not +appreciate his work at its true relative value from the very fact +that he has no great buildings or fine instruments to show. I may +therefore be allowed to claim as an important factor in the +American astronomy of the last half-century an institution of +which few have heard and which has been overlooked because there +was nothing about it to excite attention. + +In 1849 the American Nautical Almanac office was established by a +Congressional appropriation. The title of this publication is +somewhat misleading in suggesting a simple enlargement of the +family almanac which the sailor is to hang up in his cabin for +daily use. The fact is that what started more than a century ago +as a nautical almanac has since grown into an astronomical +ephemeris for the publication of everything pertaining to times, +seasons, eclipses, and the motions of the heavenly bodies. It is +the work in which astronomical observations made in all the great +observatories of the world are ultimately utilized for scientific +and public purposes. Each of the leading nations of western Europe +issues such a publication. When the preparation and publication of +the American ephemeris was decided upon the office was first +established in Cambridge, the seat of Harvard University, because +there could most readily be secured the technical knowledge of +mathematics and theoretical astronomy necessary for the work. + +A field of activity was thus opened, of which a number of able +young men who have since earned distinction in various walks of +life availed themselves. The head of the office, Commander Davis, +adopted a policy well fitted to promote their development. He +translated the classic work of Gauss, Theoria Motus Corporum +Celestium, and made the office a sort of informal school, not, +indeed, of the modern type, but rather more like the classic grove +of Hellas, where philosophers conducted their discussions and +profited by mutual attrition. When, after a few years of +experience, methods were well established and a routine adopted, +the office was removed to Washington, where it has since remained. +The work of preparing the ephemeris has, with experience, been +reduced to a matter of routine which may be continued +indefinitely, with occasional changes in methods and data, and +improvements to meet the increasing wants of investigators. + +The mere preparation of the ephemeris includes but a small part of +the work of mathematical calculation and investigation required in +astronomy. One of the great wants of the science to-day is the +reduction of the observations made during the first half of the +present century, and even during the last half of the preceding +one. The labor which could profitably be devoted to this work +would be more than that required in any one astronomical +observatory. It is unfortunate for this work that a great building +is not required for its prosecution because its needfulness is +thus very generally overlooked by that portion of the public +interested in the progress of science. An organization especially +devoted to it is one of the scientific needs of our time. + +In such an epoch-making age as the present it is dangerous to cite +any one step as making a new epoch. Yet it may be that when the +historian of the future reviews the science of our day he will +find the most remarkable feature of the astronomy of the last +twenty years of our century to be the discovery that this +steadfast earth of which the poets have told us is not, after all, +quite steadfast; that the north and south poles move about a very +little, describing curves so complicated that they have not yet +been fully marked out. The periodic variations of latitude thus +brought about were first suspected about 1880, and announced with +some modest assurance by Kustner, of Berlin, a few years later. +The progress of the views of astronomical opinion from incredulity +to confidence was extremely slow until, about 1890, Chandler, of +the United States, by an exhaustive discussion of innumerable +results of observations, showed that the latitude of every point +on the earth was subject to a double oscillation, one having a +period of a year, the other of four hundred and twenty-seven days. + +Notwithstanding the remarkable parallel between the growth of +American astronomy and that of your city, one cannot but fear that +if a foreign observer had been asked only half a dozen years ago +at what point in the United States a great school of theoretical +and practical astronomy, aided by an establishment for the +exploration of the heavens, was likely to be established by the +munificence of private citizens, he would have been wiser than +most foreigners had he guessed Chicago. Had this place been +suggested to him, I fear he would have replied that were it +possible to utilize celestial knowledge in acquiring earthly +wealth, here would be the most promising seat for such a school. +But he would need to have been a little wiser than his generation +to reflect that wealth is at the base of all progress in knowledge +and the liberal arts; that it is only when men are relieved from +the necessity of devoting all their energies to the immediate +wants of life that they can lead the intellectual life, and that +we should therefore look to the most enterprising commercial +centre as the likeliest seat for a great scientific institution. + +Now we have the school, and we have the observatory, which we hope +will in the near future do work that will cast lustre on the name +of its founder as well as on the astronomers who may be associated +with it. You will, I am sure, pardon me if I make some suggestions +on the subject of the future needs of the establishment. We want +this newly founded institution to be a great success, to do work +which shall show that the intellectual productiveness of your +community will not be allowed to lag behind its material growth +The public is very apt to feel that when some munificent patron of +science has mounted a great telescope under a suitable dome, and +supplied all the apparatus which the astronomer wants to use, +success is assured. But such is not the case. The most important +requisite, one more difficult to command than telescopes or +observatories, may still be wanting. A great telescope is of no +use without a man at the end of it, and what the telescope may do +depends more upon this appendage than upon the instrument itself. +The place which telescopes and observatories have taken in +astronomical history are by no means proportional to their +dimensions. Many a great instrument has been a mere toy in the +hands of its owner. Many a small one has become famous. + +Twenty years ago there was here in your own city a modest little +instrument which, judged by its size, could not hold up its head +with the great ones even of that day. It was the private property +of a young man holding no scientific position and scarcely known +to the public. And yet that little telescope is to-day among the +famous ones of the world, having made memorable advances in the +astronomy of double stars, and shown its owner to be a worthy +successor of the Herschels and Struves in that line of work. + +A hundred observers might have used the appliances of the Lick +Observatory for a whole generation without finding the fifth +satellite of Jupiter; without successfully photographing the cloud +forms of the Milky Way; without discovering the extraordinary +patches of nebulous light, nearly or quite invisible to the human +eye, which fill some regions of the heavens. + +When I was in Zurich last year I paid a visit to the little, but +not unknown, observatory of its famous polytechnic school. The +professor of astronomy was especially interested in the +observations of the sun with the aid of the spectroscope, and +among the ingenious devices which he described, not the least +interesting was the method of photographing the sun by special +rays of the spectrum, which had been worked out at the Kenwood +Observatory in Chicago. The Kenwood Observatory is not, I believe, +in the eye of the public, one of the noteworthy institutions of +your city which every visitor is taken to see, and yet this +invention has given it an important place in the science of our +day. + +Should you ask me what are the most hopeful features in the great +establishment which you are now dedicating, I would say that they +are not alone to be found in the size of your unequalled +telescope, nor in the cost of the outfit, but in the fact that +your authorities have shown their appreciation of the requirements +of success by adding to the material outfit of the establishment +the three men whose works I have described. + +Gentlemen of the trustees, allow me to commend to your fostering +care the men at the end of the telescope. The constitution of the +astronomer shows curious and interesting features. If he is +destined to advance the science by works of real genius, he must, +like the poet, be born, not made. The born astronomer, when placed +in command of a telescope, goes about using it as naturally and +effectively as the babe avails itself of its mother's breast. He +sees intuitively what less gifted men have to learn by long study +and tedious experiment. He is moved to celestial knowledge by a +passion which dominates his nature. He can no more avoid doing +astronomical work, whether in the line of observations or +research, than a poet can chain his Pegasus to earth. I do not +mean by this that education and training will be of no use to him. +They will certainly accelerate his early progress. If he is to +become great on the mathematical side, not only must his genius +have a bend in that direction, but he must have the means of +pursuing his studies. And yet I have seen so many failures of men +who had the best instruction, and so many successes of men who +scarcely learned anything of their teachers, that I sometimes ask +whether the great American celestial mechanician of the twentieth +century will be a graduate of a university or of the backwoods. + +Is the man thus moved to the exploration of nature by an +unconquerable passion more to be envied or pitied? In no other +pursuit does success come with such certainty to him who deserves +it. No life is so enjoyable as that whose energies are devoted to +following out the inborn impulses of one's nature. The +investigator of truth is little subject to the disappointments +which await the ambitious man in other fields of activity. It is +pleasant to be one of a brotherhood extending over the world, in +which no rivalry exists except that which comes out of trying to +do better work than any one else, while mutual admiration stifles +jealousy. And yet, with all these advantages, the experience of +the astronomer may have its dark side. As he sees his field +widening faster than he can advance he is impressed with the +littleness of all that can be done in one short life. He feels the +same want of successors to pursue his work that the founder of a +dynasty may feel for heirs to occupy his throne. He has no desire +to figure in history as a Napoleon of science whose conquests must +terminate with his life. Even during his active career his work +may be such a kind as to require the co-operation of others and +the active support of the public. If he is disappointed in +commanding these requirements, if he finds neither co-operation +nor support, if some great scheme to which he may have devoted +much of his life thus proves to be only a castle in the air, he +may feel that nature has dealt hardly with him in not endowing him +with passions like to those of other men. + +In treating a theme of perennial interest one naturally tries to +fancy what the future may have in store If the traveller, +contemplating the ruins of some ancient city which in the long ago +teemed with the life and activities of generations of men, sees +every stone instinct with emotion and the dust alive with memories +of the past, may he not be similarly impressed when he feels that +he is looking around upon a seat of future empire--a region where +generations yet unborn may take a leading part in moulding the +history of the world? What may we not expect of that energy which +in sixty years has transformed a straggling village into one of +the world's great centres of commerce? May it not exercise a +powerful influence on the destiny not only of the country but of +the world? If so, shall the power thus to be exercised prove an +agent of beneficence, diffusing light and life among nations, or +shall it be the opposite? + +The time must come ere long when wealth shall outgrow the field in +which it can be profitably employed. In what direction shall its +possessors then look? Shall they train a posterity which will so +use its power as to make the world better that it has lived in it? +Will the future heir to great wealth prefer the intellectual life +to the life of pleasure? + +We can have no more hopeful answer to these questions than the +establishment of this great university in the very focus of the +commercial activity of the West. Its connection with the +institution we have been dedicating suggests some thoughts on +science as a factor in that scheme of education best adapted to +make the power of a wealthy community a benefit to the race at +large. When we see what a factor science has been in our present +civilization, how it has transformed the world and increased the +means of human enjoyment by enabling men to apply the powers of +nature to their own uses, it is not wonderful that it should claim +the place in education hitherto held by classical studies. In the +contest which has thus arisen I take no part but that of a peace- +maker, holding that it is as important to us to keep in touch with +the traditions of our race, and to cherish the thoughts which have +come down to us through the centuries, as it is to enjoy and +utilize what the present has to offer us. Speaking from this point +of view, I would point out the error of making the utilitarian +applications of knowledge the main object in its pursuit. It is an +historic fact that abstract science--science pursued without any +utilitarian end--has been at the base of our progress in the +utilization of knowledge. If in the last century such men as +Galvani and Volta had been moved by any other motive than love of +penetrating the secrets of nature they would never have pursued +the seemingly useless experiments they did, and the foundation of +electrical science would not have been laid. Our present +applications of electricity did not become possible until Ohm's +mathematical laws of the electric current, which when first made +known seemed little more than mathematical curiosities, had become +the common property of inventors. Professional pride on the part +of our own Henry led him, after making the discoveries which +rendered the telegraph possible, to go no further in their +application, and to live and die without receiving a dollar of the +millions which the country has won through his agency. + +In the spirit of scientific progress thus shown we have patriotism +in its highest form--a sentiment which does not seek to benefit +the country at the expense of the world, but to benefit the world +by means of one's country. Science has its competition, as keen as +that which is the life of commerce. But its rivalries are over the +question who shall contribute the most and the best to the sum +total of knowledge; who shall give the most, not who shall take +the most. Its animating spirit is love of truth. Its pride is to +do the greatest good to the greatest number. It embraces not only +the whole human race but all nature in its scope. The public +spirit of which this city is the focus has made the desert blossom +as the rose, and benefited humanity by the diffusion of the +material products of the earth. Should you ask me how it is in the +future to use its influence for the benefit of humanity at large, +I would say, look at the work now going on in these precincts, and +study its spirit. Here are the agencies which will make "the voice +of law the harmony of the world." Here is the love of country +blended with love of the race. Here the love of knowledge is as +unconfined as your commercial enterprise. Let not your youth come +hither merely to learn the forms of vertebrates and the properties +of oxides, but rather to imbibe that catholic spirit which, +animating their growing energies, shall make the power they are to +wield an agent of beneficence to all mankind. + + + + + +XIX + +THE UNIVERSE AS AN ORGANISM + +[Footnote: Address before the Astronomical and Astrophysical +Society of America, December 29, 1902] + + +If I were called upon to convey, within the compass of a single +sentence, an idea of the trend of recent astronomical and physical +science, I should say that it was in the direction of showing the +universe to be a connected whole. The farther we advance in +knowledge, the clearer it becomes that the bodies which are +scattered through the celestial spaces are not completely +independent existences, but have, with all their infinite +diversity, many attributes in common. + +In this we are going in the direction of certain ideas of the +ancients which modern discovery long seemed to have contradicted. +In the infancy of the race, the idea that the heavens were simply +an enlarged and diversified earth, peopled by beings who could +roam at pleasure from one extreme to the other, was a quite +natural one. The crystalline sphere or spheres which contained all +formed a combination of machinery revolving on a single plan. But +all bonds of unity between the stars began to be weakened when +Copernicus showed that there were no spheres, that the planets +were isolated bodies, and that the stars were vastly more distant +than the planets. As discovery went on and our conceptions of the +universe were enlarged, it was found that the system of the fixed +stars was made up of bodies so vastly distant and so completely +isolated that it was difficult to conceive of them as standing in +any definable relation to one another. It is true that they all +emitted light, else we could not see them, and the theory of +gravitation, if extended to such distances, a fact not then +proved, showed that they acted on one another by their mutual +gravitation. But this was all. Leaving out light and gravitation, +the universe was still, in the time of Herschel, composed of +bodies which, for the most part, could not stand in any known +relation one to the other. + +When, forty years ago, the spectroscope was applied to analyze the +light coming from the stars, a field was opened not less fruitful +than that which the telescope made known to Galileo. The first +conclusion reached was that the sun was composed almost entirely +of the same elements that existed upon the earth. Yet, as the +bodies of our solar system were evidently closely related, this +was not remarkable. But very soon the same conclusion was, to a +limited extent, extended to the fixed stars in general. Such +elements as iron, hydrogen, and calcium were found not to belong +merely to our earth, but to form important constituents of the +whole universe. We can conceive of no reason why, out of the +infinite number of combinations which might make up a spectrum, +there should not be a separate kind of matter for each +combination. So far as we know, the elements might merge into one +another by insensible gradations. It is, therefore, a remarkable +and suggestive fact when we find that the elements which make up +bodies so widely separate that we can hardly imagine them having +anything in common, should be so much the same. + +In recent times what we may regard as a new branch of astronomical +science is being developed, showing a tendency towards unity of +structure throughout the whole domain of the stars. This is what +we now call the science of stellar statistics. The very conception +of such a science might almost appall us by its immensity. The +widest statistical field in other branches of research is that +occupied by sociology. Every country has its census, in which the +individual inhabitants are classified on the largest scale and the +combination of these statistics for different countries may be +said to include all the interest of the human race within its +scope. Yet this field is necessarily confined to the surface of +our planet. In the field of stellar statistics millions of stars +are classified as if each taken individually were of no more +weight in the scale than a single inhabitant of China in the scale +of the sociologist. And yet the most insignificant of these suns +may, for aught we know, have planets revolving around it, the +interests of whose inhabitants cover as wide a range as ours do +upon our own globe. + +The statistics of the stars may be said to have commenced with +Herschel's gauges of the heavens, which were continued from time +to time by various observers, never, however, on the largest +scale. The subject was first opened out into an illimitable field +of research through a paper presented by Kapteyn to the Amsterdam +Academy of Sciences in 1893. The capital results of this paper +were that different regions of space contain different kinds of +stars and, more especially, that the stars of the Milky Way +belong, in part at least, to a different class from those existing +elsewhere. Stars not belonging to the Milky Way are, in large +part, of a distinctly different class. + +The outcome of Kapteyn's conclusions is that we are able to +describe the universe as a single object, with some characters of +an organized whole. A large part of the stars which compose it may +be considered as divisible into two groups. One of these comprises +the stars composing the great girdle of the Milky Way. These are +distinguished from the others by being bluer in color, generally +greater in absolute brilliancy, and affected, there is some reason +to believe, with rather slower proper motions The other classes +are stars with a greater or less shade of yellow in their color, +scattered through a spherical space of unknown dimensions, but +concentric with the Milky Way. Thus a sphere with a girdle passing +around it forms the nearest approach to a conception of the +universe which we can reach to-day. The number of stars in the +girdle is much greater than that in the sphere. + +The feature of the universe which should therefore command our +attention is the arrangement of a large part of the stars which +compose it in a ring, seemingly alike in all its parts, so far as +general features are concerned. So far as research has yet gone, +we are not able to say decisively that one region of this ring +differs essentially from another. It may, therefore, be regarded +as forming a structure built on a uniform plan throughout. + +All scientific conclusions drawn from statistical data require a +critical investigation of the basis on which they rest. If we are +going, from merely counting the stars, observing their magnitudes +and determining their proper motions, to draw conclusions as to +the structure of the universe in space, the question may arise how +we can form any estimate whatever of the possible distance of the +stars, a conclusion as to which must be the very first step we +take. We can hardly say that the parallaxes of more than one +hundred stars have been measured with any approach to certainty. +The individuals of this one hundred are situated at very different +distances from. us. We hope, by long and repeated observations, to +make a fairly approximate determination of the parallaxes of all +the stars whose distance is less than twenty times that of a +Centauri. But how can we know anything about the distance of stars +outside this sphere? What can we say against the view of Kepler +that the space around our sun is very much thinner in stars than +it is at a greater distance; in fact, that, the great mass of the +stars may be situated between the surfaces of two concentrated +spheres not very different in radius. May not this universe of +stars be somewhat in the nature of a hollow sphere? + +This objection requires very careful consideration on the part of +all who draw conclusions as to the distribution of stars in space +and as to the extent of the visible universe. The steps to a +conclusion on the subject are briefly these: First, we have a +general conclusion, the basis of which I have already set forth, +that, to use a loose expression, there are likenesses throughout +the whole diameter of the universe. There is, therefore, no reason +to suppose that the region in which our system is situated differs +in any essential degree from any other region near the central +portion. Again, spectroscopic examinations seem to show that all +the stars are in motion, and that we cannot say that those in one +part of the universe move more rapidly than those in another. This +result is of the greatest value for our purpose, because, when we +consider only the apparent motions, as ordinarily observed, these +are necessarily dependent upon the distance of the star. We +cannot, therefore, infer the actual speed of a star from ordinary +observations until we know its distance. But the results of +spectroscopic measurements of radial velocity are independent of +the distance of the star. + +But let us not claim too much. We cannot yet say with certainty +that the stars which form the agglomerations of the Milky Way +have, beyond doubt, the same average motion as the stars in other +regions of the universe. The difficulty is that these stars appear +to us so faint individually, that the investigation of their +spectra is still beyond the powers of our instruments. But the +extraordinary feat performed at the Lick Observatory of measuring +the radial motion of 1830 Groombridge, a star quite invisible to +the naked eye, and showing that it is approaching our system with +a speed of between fifty and sixty miles a second, may lead us to +hope for a speedy solution of this question. But we need not await +this result in order to reach very probable conclusions. The +general outcome of researches on proper motions tends to +strengthen the conclusions that the Keplerian sphere, if I may use +this expression, has no very well marked existence. The laws of +stellar velocity and the statistics of proper motions, while +giving some color to the view that the space in which we are +situated is thinner in stars than elsewhere, yet show that, as a +general rule, there are no great agglomerations of stars elsewhere +than in the region of the Milky Way. + +With unity there is always diversity; in fact, the unity of the +universe on which I have been insisting consists in part of +diversity. It is very curious that, among the many thousands of +stars which have been spectroscopically examined, no two are known +to have absolutely the same physical constitution. It is true that +there are a great many resemblances. a Centauri, our nearest +neighbor, if we can use such a word as "near" in speaking of its +distance, has a spectrum very like that of our sun, and so has +Capella. But even in these cases careful examination shows +differences. These differences arise from variety in the +combinations and temperature of the substances of which the star +is made up. Quite likely also, elements not known on the earth may +exist on the stars, but this is a point on which we cannot yet +speak with certainty. + +Perhaps the attribute in which the stars show the greatest variety +is that of absolute luminosity. One hundred years ago it was +naturally supposed that the brighter stars were the nearest to us, +and this is doubtless true when we take the general average. But +it was soon found that we cannot conclude that because a star is +bright, therefore it is near. The most striking example of this is +afforded by the absence of measurable parallaxes in the two bright +stars, Canopus and Rigel, showing that these stars, though of the +first magnitude, are immeasurably distant. A remarkable fact is +that these conclusions coincide with that which we draw from the +minuteness of the proper motions. Rigel has no motion that has +certainly been shown by more than a century of observation, and it +is not certain that Canopus has either. From this alone we may +conclude, with a high degree of probability, that the distance of +each is immeasurably great. We may say with certainty that the +brightness of each is thousands of times that of the sun, and with +a high degree of probability that it is hundreds of thousands of +times. On the other hand, there are stars comparatively near us of +which the light is not the hundredth part of the sun. + +[Illustration with caption: Star Spectra] + +The universe may be a unit in two ways. One is that unity of +structure to which our attention has just been directed. This +might subsist forever without one body influencing another. The +other form of unity leads us to view the universe as an organism. +It is such by mutual action going on between its bodies. A few +years ago we could hardly suppose or imagine that any other agents +than gravitation and light could possibly pass through spaces so +immense as those which separate the stars. + +The most remarkable and hopeful characteristic of the unity of the +universe is the evidence which is being gathered that there are +other agencies whose exact nature is yet unknown to us, but which +do pass from one heavenly body to another. The best established +example of this yet obtained is afforded in the case of the sun +and the earth. + +The fact that the frequency of magnetic storms goes through a +period of about eleven years, and is proportional to the frequency +of sun-spots, has been well established. The recent work of +Professor Bigelow shows the coincidence to be of remarkable +exactness, the curves of the two phenomena being practically +coincident so far as their general features are concerned. The +conclusion is that spots on the sun and magnetic storms are due to +the same cause. This cause cannot be any change in the ordinary +radiation of the sun, because the best records of temperature show +that, to whatever variations the sun's radiation may be subjected, +they do not change in the period of the sun-spots. To appreciate +the relation, we must recall that the researches of Hale with the +spectro-heliograph show that spots are not the primary phenomenon +of solar activity, but are simply the outcome of processes going +on constantly in the sun which result in spots only in special +regions and on special occasions. It does not, therefore, +necessarily follow that a spot does cause a magnetic storm. What +we should conclude is that the solar activity which produces a +spot also produces the magnetic storm. + +When we inquire into the possible nature of these relations +between solar activity and terrestrial magnetism, we find +ourselves so completely in the dark that the question of what is +really proved by the coincidence may arise. Perhaps the most +obvious explanation of fluctuations in the earth's magnetic field +to be inquired into would be based on the hypothesis that the +space through which the earth is moving is in itself a varying +magnetic field of vast extent. This explanation is tested by +inquiring whether the fluctuations in question can be explained by +supposing a disturbing force which acts substantially in the same +direction all over the globe. But a very obvious test shows that +this explanation is untenable. Were it the correct one, the +intensity of the force in some regions of the earth would be +diminished and in regions where the needle pointed in the opposite +direction would be increased in exactly the same degree. But there +is no relation traceable either in any of the regular fluctuations +of the magnetic force, or in those irregular ones which occur +during a magnetic storm. If the horizontal force is increased in +one part of the earth, it is very apt to show a simultaneous +increase the world over, regardless of the direction in which the +needle may point in various localities. It is hardly necessary to +add that none of the fluctuations in terrestrial magnetism can be +explained on the hypothesis that either the moon or the sun acts +as a magnet. In such a case the action would be substantially in +the same direction at the same moment the world over. + +Such being the case, the question may arise whether the action +producing a magnetic storm comes from the sun at all, and whether +the fluctuations in the sun's activity, and in the earth's +magnetic field may not be due to some cause external to both. All +we can say in reply to this is that every effort to find such a +cause has failed and that it is hardly possible to imagine any +cause producing such an effect. It is true that the solar spots +were, not many years ago, supposed to be due in some way to the +action of the planets. But, for reasons which it would be tedious +to go into at present, we may fairly regard this hypothesis as +being completely disproved. There can, I conclude, be little doubt +that the eleven-year cycle of change in the solar spots is due to +a cycle going on in the sun itself. Such being the case, the +corresponding change in the earth's magnetism must be due to the +same cause. + +We may, therefore, regard it as a fact sufficiently established to +merit further investigation that there does emanate from the sun, +in an irregular way, some agency adequate to produce a measurable +effect on the magnetic needle. We must regard it as a singular +fact that no observations yet made give us the slightest +indication as to what this emanation is. The possibility of +defining it is suggested by the discovery within the past few +years, that under certain conditions, heated matter sends forth +entities known as Rontgen rays, Becquerel corpuscles and +electrons. I cannot speak authoritatively on this subject, but, so +far as I am aware, no direct evidence has yet been gathered +showing that any of these entities reach us from the sun. We must +regard the search for the unknown agency so fully proved as among +the most important tasks of the astronomical physicist of the +present time. From what we know of the history of scientific +discovery, it seems highly probable that, in the course of his +search, he will, before he finds the object he is aiming at, +discover many other things of equal or greater importance of which +he had, at the outset, no conception. + +The main point I desire to bring out in this review is the +tendency which it shows towards unification in physical research. +Heretofore differentiation--the subdivision of workers into a +continually increasing number of groups of specialists--has been +the rule. Now we see a coming together of what, at first sight, +seem the most widely separated spheres of activity. What two +branches could be more widely separated than that of stellar +statistics, embracing the whole universe within its scope, and the +study of these newly discovered emanations, the product of our +laboratories, which seem to show the existence of corpuscles +smaller than the atoms of matter? And yet, the phenomena which we +have reviewed, especially the relation of terrestrial magnetism to +the solar activity, and the formation of nebulous masses around +the new stars, can be accounted for only by emanations or forms of +force, having probably some similarity with the corpuscles, +electrons, and rays which we are now producing in our +laboratories. The nineteenth century, in passing away, points with +pride to what it has done. It has become a word to symbolize what +is most important in human progress Yet, perhaps its greatest +glory may prove to be that the last thing it did was to lay a +foundation for the physical science of the twentieth century. What +shall be discovered in the new fields is, at present, as far +without our ken as were the modern developments of electricity +without the ken of the investigators of one hundred years ago. We +cannot guarantee any special discovery. What lies before us is an +illimitable field, the existence of which was scarcely suspected +ten years ago, the exploration of which may well absorb the +activities of our physical laboratories, and of the great mass of +our astronomical observers and investigators for as many +generations as were required to bring electrical science to its +present state. We of the older generation cannot hope to see more +than the beginning of this development, and can only tender our +best wishes and most hearty congratulations to the younger school +whose function it will be to explore the limitless field now +before it. + + + + + +XX + +THE RELATION OF SCIENTIFIC METHOD TO SOCIAL PROGRESS +[Footnote: An address before the Washington Philosophical Society] + + +Among those subjects which are not always correctly apprehended, +even by educated men, we may place that of the true significance +of scientific method and the relations of such method to practical +affairs. This is especially apt to be the case in a country like +our own, where the points of contact between the scientific world +on the one hand, and the industrial and political world on the +other, are fewer than in other civilized countries. The form which +this misapprehension usually takes is that of a failure to +appreciate the character of scientific method, and especially its +analogy to the methods of practical life. In the judgment of the +ordinary intelligent man there is a wide distinction between +theoretical and practical science. The latter he considers as that +science directly applicable to the building of railroads, the +construction of engines, the invention of new machinery, the +construction of maps, and other useful objects. The former he +considers analogous to those philosophic speculations in which men +have indulged in all ages without leading to any result which he +considers practical. That our knowledge of nature is increased by +its prosecution is a fact of which he is quite conscious, but he +considers it as terminating with a mere increase of knowledge, and +not as having in its method anything which a person devoted to +material interests can be expected to appreciate. + +This view is strengthened by the spirit with which he sees +scientific investigation prosecuted. It is well understood on all +sides that when such investigations are pursued in a spirit really +recognized as scientific, no merely utilitarian object is had in +view. Indeed, it is easy to see how the very fact of pursuing such +an object would detract from that thoroughness of examination +which is the first condition of a real advance. True science +demands in its every research a completeness far beyond what is +apparently necessary for its practical applications. The precision +with which the astronomer seeks to measure the heavens and the +chemist to determine the relations of the ultimate molecules of +matter has no limit, except that set by the imperfections of the +instruments of research. There is no such division recognized as +that of useful and useless knowledge. The ultimate aim is nothing +less than that of bringing all the phenomena of nature under laws +as exact as those which govern the planetary motions. + +Now the pursuit of any high object in this spirit commands from +men of wide views that respect which is felt towards all exertion +having in view more elevated objects than the pursuit of gain. +Accordingly, it is very natural to classify scientists and +philosophers with the men who in all ages have sought after +learning instead of utility. But there is another aspect of the +question which will show the relations of scientific advance to +the practical affairs of life in a different light. I make bold to +say that the greatest want of the day, from a purely practical +point of view, is the more general introduction of the scientific +method and the scientific spirit into the discussion of those +political and social problems which we encounter on our road to a +higher plane of public well being. Far from using methods too +refined for practical purposes, what most distinguishes scientific +from other thought is the introduction of the methods of practical +life into the discussion of abstract general problems. A single +instance will illustrate the lesson I wish to enforce. + +The question of the tariff is, from a practical point of view, one +of the most important with which our legislators will have to deal +during the next few years. The widest diversity of opinion exists +as to the best policy to be pursued in collecting a revenue from +imports. Opposing interests contend against one another without +any common basis of fact or principle on which a conclusion can be +reached. The opinions of intelligent men differ almost as widely +as those of the men who are immediately interested. But all will +admit that public action in this direction should be dictated by +one guiding principle--that the greatest good of the community is +to be sought after. That policy is the best which will most +promote this good. Nor is there any serious difference of opinion +as to the nature of the good to be had in view; it is in a word +the increase of the national wealth and prosperity. The question +on which opinions fundamentally differ is that of the effects of a +higher or lower rate of duty upon the interests of the public. If +it were possible to foresee, with an approach to certainty, what +effect a given tariff would have upon the producers and consumers +of an article taxed, and, indirectly, upon each member of the +community in any way interested in the article, we should then +have an exact datum which we do not now possess for reaching a +conclusion. If some superhuman authority, speaking with the voice +of infallibility, could give us this information, it is evident +that a great national want would be supplied. No question in +practical life is more important than this: How can this desirable +knowledge of the economic effects of a tariff be obtained? + +The answer to this question is clear and simple. The subject must +be studied in the same spirit, and, to a certain extent, by the +same methods which have been so successful in advancing our +knowledge of nature. Every one knows that, within the last two +centuries, a method of studying the course of nature has been +introduced which has been so successful in enabling us to trace +the sequence of cause and effect as almost to revolutionize +society. The very fact that scientific method has been so +successful here leads to the belief that it might be equally +successful in other departments of inquiry. + +The same remarks will apply to the questions connected with +banking and currency; the standard of value; and, indeed, all +subjects which have a financial bearing. On every such question we +see wide differences of opinion without any common basis to rest +upon. + +It may be said, in reply, that in these cases there are really no +grounds for forming an opinion, and that the contests which arise +over them are merely those between conflicting interests. But this +claim is not at all consonant with the form which we see the +discussion assume. Nearly every one has a decided opinion on these +several subjects; whereas, if there were no data for forming an +opinion, it would be unreasonable to maintain any whatever. +Indeed, it is evident that there must be truth somewhere, and the +only question that can be open is that of the mode of discovering +it. No man imbued with a scientific spirit can claim that such +truth is beyond the power of the human intellect. He may doubt his +own ability to grasp it, but cannot doubt that by pursuing the +proper method and adopting the best means the problem can be +solved. It is, in fact, difficult to show why some exact results +could not be as certainly reached in economic questions as in +those of physical science. It is true that if we pursue the +inquiry far enough we shall find more complex conditions to +encounter, because the future course of demand and supply enters +as an uncertain element. But a remarkable fact to be considered is +that the difference of opinion to which we allude does not depend +upon different estimates of the future, but upon different views +of the most elementary and general principles of the subject. It +is as if men were not agreed whether air were elastic or whether +the earth turns on its axis. Why is it that while in all subjects +of physical science we find a general agreement through a wide +range of subjects, and doubt commences only where certainty is not +attained, yet when we turn to economic subjects we do not find the +beginning of an agreement? + +No two answers can be given. It is because the two classes of +subjects are investigated by different instruments and in a +different spirit. The physicist has an exact nomenclature; uses +methods of research well adapted to the objects he has in view; +pursues his investigations without being attacked by those who +wish for different results; and, above all, pursues them only for +the purpose of discovering the truth. In economic questions the +case is entirely different. Only in rare cases are they studied +without at least the suspicion that the student has a preconceived +theory to support. If results are attained which oppose any +powerful interest, this interest can hire a competing investigator +to bring out a different result. So far as the public can see, one +man's result is as good as another's, and thus the object is as +far off as ever. We may be sure that until there is an intelligent +and rational public, able to distinguish between the speculations +of the charlatan and the researches of the investigator, the +present state of things will continue. What we want is so wide a +diffusion of scientific ideas that there shall be a class of men +engaged in studying economic problems for their own sake, and an +intelligent public able to judge what they are doing. There must +be an improvement in the objects at which they aim in education, +and it is now worth while to inquire what that improvement is. + +It is not mere instruction in any branch of technical science that +is wanted. No knowledge of chemistry, physics, or biology, however +extensive, can give the learner much aid in forming a correct +opinion of such a question as that of the currency. If we should +claim that political economy ought to be more extensively studied, +we would be met by the question, which of several conflicting +systems shall we teach? What is wanted is not to teach this system +or that, but to give such a training that the student shall be +able to decide for himself which system is right. + +It seems to me that the true educational want is ignored both by +those who advocate a classical and those who advocate a scientific +education. What is really wanted is to train the intellectual +powers, and the question ought to be, what is the best method of +doing this? Perhaps it might be found that both of the conflicting +methods could be improved upon. The really distinctive features, +which we should desire to see introduced, are two in number: the +one the scientific spirit; the other the scientific discipline. +Although many details may be classified under each of these heads, +yet there is one of pre-eminent importance on which we should +insist. + +The one feature of the scientific spirit which outweighs all +others in importance is the love of knowledge for its own sake. If +by our system of education we can inculcate this sentiment we +shall do what is, from a public point of view, worth more than any +amount of technical knowledge, because we shall lay the foundation +of all knowledge. So long as men study only what they think is +going to be useful their knowledge will be partial and +insufficient. I think it is to the constant inculcation of this +fact by experience, rather than to any reasoning, that is due the +continued appreciation of a liberal education. Every business-man +knows that a business-college training is of very little account +in enabling one to fight the battle of life, and that college-bred +men have a great advantage even in fields where mere education is +a secondary matter. We are accustomed to seeing ridicule thrown +upon the questions sometimes asked of candidates for the civil +service because the questions refer to subjects of which a +knowledge is not essential. The reply to all criticisms of this +kind is that there is no one quality which more certainly assures +a man's usefulness to society than the propensity to acquire +useless knowledge. Most of our citizens take a wide interest in +public affairs, else our form of government would be a failure. +But it is desirable that their study of public measures should be +more critical and take a wider range. It is especially desirable +that the conclusions to which they are led should be unaffected by +partisan sympathies. The more strongly the love of mere truth is +inculcated in their nature the better this end will be attained. + +The scientific discipline to which I ask mainly to call your +attention consists in training the scholar to the scientific use +of language. Although whole volumes may be written on the logic of +science there is one general feature of its method which is of +fundamental significance. It is that every term which it uses and +every proposition which it enunciates has a precise meaning which +can be made evident by proper definitions. This general principle +of scientific language is much more easily inculcated by example +than subject to exact description; but I shall ask leave to add +one to several attempts I have made to define it. If I should say +that when a statement is made in the language of science the +speaker knows what he means, and the hearer either knows it or can +be made to know it by proper definitions, and that this community +of understanding is frequently not reached in other departments of +thought, I might be understood as casting a slur on whole +departments of inquiry. Without intending any such slur, I may +still say that language and statements are worthy of the name +scientific as they approach this standard; and, moreover, that a +great deal is said and written which does not fulfil the +requirement. The fact that words lose their meaning when removed +from the connections in which that meaning has been acquired and +put to higher uses, is one which, I think, is rarely recognized. +There is nothing in the history of philosophical inquiry more +curious than the frequency of interminable disputes on subjects +where no agreement can be reached because the opposing parties do +not use words in the same sense. That the history of science is +not free from this reproach is shown by the fact of the long +dispute whether the force of a moving body was proportional to the +simple velocity or to its square. Neither of the parties to the +dispute thought it worth while to define what they meant by the +word "force," and it was at length found that if a definition was +agreed upon the seeming difference of opinion would vanish. +Perhaps the most striking feature of the case, and one peculiar to +a scientific dispute, was that the opposing parties did not differ +in their solution of a single mechanical problem. I say this is +curious, because the very fact of their agreeing upon every +concrete question which could have been presented ought to have +made it clear that some fallacy was lacking in the discussion as +to the measure of force. The good effect of a scientific spirit is +shown by the fact that this discussion is almost unique in the +history of science during the past two centuries, and that +scientific men themselves were able to see the fallacy involved, +and thus to bring the matter to a conclusion. + +If we now turn to the discussion of philosophers, we shall find at +least one yet more striking example of the same kind. The question +of the freedom of the human will has, I believe, raged for +centuries. It cannot yet be said that any conclusion has been +reached. Indeed, I have heard it admitted by men of high +intellectual attainments that the question was insoluble. Now a +curious feature of this dispute is that none of the combatants, at +least on the affirmative side, have made any serious attempt to +define what should be meant by the phrase freedom of the will, +except by using such terms as require definition equally with the +word freedom itself. It can, I conceive, be made quite clear that +the assertion, "The will is free," is one without meaning, until +we analyze more fully the different meanings to be attached to the +word free. Now this word has a perfectly well-defined +signification in every-day life. We say that anything is free when +it is not subject to external constraint. We also know exactly +what we mean when we say that a man is free to do a certain act. +We mean that if he chooses to do it there is no external +constraint acting to prevent him. In all cases a relation of two +things is implied in the word, some active agent or power, and the +presence or absence of another constraining agent. Now, when we +inquire whether the will itself is free, irrespective of external +constraints, the word free no longer has a meaning, because one of +the elements implied in it is ignored. + +To inquire whether the will itself is free is like inquiring +whether fire itself is consumed by the burning, or whether +clothing is itself clad. It is not, therefore, at all surprising +that both parties have been able to dispute without end, but it is +a most astonishing phenomenon of the human intellect that the +dispute should go on generation after generation without the +parties finding out whether there was really any difference of +opinion between them on the subject. I venture to say that if +there is any such difference, neither party has ever analyzed the +meaning of the words used sufficiently far to show it. The daily +experience of every man, from his cradle to his grave, shows that +human acts are as much the subject of external causal influences +as are the phenomena of nature. To dispute this would be little +short of the ludicrous. All that the opponents of freedom, as a +class, have ever claimed is the assertion of a causal connection +between the acts of the will and influences independent of the +will. True, propositions of this sort can be expressed in a +variety of ways connoting an endless number of more or less +objectionable ideas, but this is the substance of the matter. + +To suppose that the advocates on the other side meant to take +issue on this proposition would be to assume that they did not +know what they were saying. The conclusion forced upon us is that +though men spend their whole lives in the study of the most +elevated department of human thought it does not guard them +against the danger of using words without meaning. It would be a +mark of ignorance, rather than of penetration, to hastily denounce +propositions on subjects we are not well acquainted with because +we do not understand their meaning. I do not mean to intimate that +philosophy itself is subject to this reproach. When we see a +philosophical proposition couched in terms we do not understand, +the most modest and charitable view is to assume that this arises +from our lack of knowledge. Nothing is easier than for the +ignorant to ridicule the propositions of the learned. And yet, +with every reserve, I cannot but feel that the disputes to which I +have alluded prove the necessity of bringing scientific precision +of language into the whole domain of thought. If the discussion +had been confined to a few, and other philosophers had analyzed +the subject, and showed the fictitious character of the +discussion, or had pointed out where opinions really might differ, +there would be nothing derogatory to philosophers. But the most +suggestive circumstance is that although a large proportion of the +philosophic writers in recent times have devoted more or less +attention to the subject, few, or none, have made even this modest +contribution. I speak with some little confidence on this subject, +because several years ago I wrote to one of the most acute +thinkers of the country, asking if he could find in philosophic +literature any terms or definitions expressive of the three +different senses in which not only the word freedom, but nearly +all words implying freedom were used. His search was in vain. + +Nothing of this sort occurs in the practical affairs of life. All +terms used in business, however general or abstract, have that +well-defined meaning which is the first requisite of the +scientific language. Now one important lesson which I wish to +inculcate is that the language of science in this respect +corresponds to that of business; in that each and every term that +is employed has a meaning as well defined as the subject of +discussion can admit of. It will be an instructive exercise to +inquire what this peculiarity of scientific and business language +is. It can be shown that a certain requirement should be fulfilled +by all language intended for the discovery of truth, which is +fulfilled only by the two classes of language which I have +described. It is one of the most common errors of discourse to +assume that any common expression which we may use always conveys +an idea, no matter what the subject of discourse. The true state +of the case can, perhaps, best be seen by beginning at the +foundation of things and examining under what conditions language +can really convey ideas. + +Suppose thrown among us a person of well-developed intellect, but +unacquainted with a single language or word that we use. It is +absolutely useless to talk to him, because nothing that we say +conveys any meaning to his mind. We can supply him no dictionary, +because by hypothesis he knows no language to which we have +access. How shall we proceed to communicate our ideas to him? +Clearly there is but one possible way--namely, through his senses. +Outside of this means of bringing him in contact with us we can +have no communication with him. We, therefore, begin by showing +him sensible objects, and letting him understand that certain +words which we use correspond to those objects. After he has thus +acquired a small vocabulary, we make him understand that other +terms refer to relations between objects which he can perceive by +his senses. Next he learns, by induction, that there are terms +which apply not to special objects, but to whole classes of +objects. Continuing the same process, he learns that there are +certain attributes of objects made known by the manner in which +they affect his senses, to which abstract terms are applied. +Having learned all this, we can teach him new words by combining +words without exhibiting objects already known. Using these words +we can proceed yet further, building up, as it were, a complete +language. But there is one limit at every step. Every term which +we make known to him must depend ultimately upon terms the meaning +of which he has learned from their connection with special objects +of sense. + +To communicate to him a knowledge of words expressive of mental +states it is necessary to assume that his own mind is subject to +these states as well as our own, and that we can in some way +indicate them by our acts. That the former hypothesis is +sufficiently well established can be made evident so long as a +consistency of different words and ideas is maintained. If no such +consistency of meaning on his part were evident, it might indicate +that the operations of his mind were so different from ours that +no such communication of ideas was possible. Uncertainty in this +respect must arise as soon as we go beyond those mental states +which communicate themselves to the senses of others. + +We now see that in order to communicate to our foreigner a +knowledge of language, we must follow rules similar to those +necessary for the stability of a building. The foundation of the +building must be well laid upon objects knowable by his five +senses. Of course the mind, as well as the external object, may be +a factor in determining the ideas which the words are intended to +express; but this does not in any manner invalidate the conditions +which we impose. Whatever theory we may adopt of the relative part +played by the knowing subject, and the external object in the +acquirement of knowledge, it remains none the less true that no +knowledge of the meaning of a word can be acquired except through +the senses, and that the meaning is, therefore, limited by the +senses. If we transgress the rule of founding each meaning upon +meanings below it, and having the whole ultimately resting upon a +sensuous foundation, we at once branch off into sound without +sense. We may teach him the use of an extended vocabulary, to the +terms of which he may apply ideas of his own, more or less vague, +but there will be no way of deciding that he attaches the same +meaning to these terms that we do. + +What we have shown true of an intelligent foreigner is necessarily +true of the growing child. We come into the world without a +knowledge of the meaning of words, and can acquire such knowledge +only by a process which we have found applicable to the +intelligent foreigner. But to confine ourselves within these +limits in the use of language requires a course of severe mental +discipline. The transgression of the rule will naturally seem to +the undisciplined mind a mark of intellectual vigor rather than +the reverse. In our system of education every temptation is held +out to the learner to transgress the rule by the fluent use of +language to which it is doubtful if he himself attaches clear +notions, and which he can never be certain suggests to his hearer +the ideas which he desires to convey. Indeed, we not infrequently +see, even among practical educators, expressions of positive +antipathy to scientific precision of language so obviously opposed +to good sense that they can be attributed only to a failure to +comprehend the meaning of the language which they criticise. + +Perhaps the most injurious effect in this direction arises from +the natural tendency of the mind, when not subject to a scientific +discipline, to think of words expressing sensible objects and +their relations as connoting certain supersensuous attributes. +This is frequently seen in the repugnance of the metaphysical mind +to receive a scientific statement about a matter of fact simply as +a matter of fact. This repugnance does not generally arise in +respect to the every-day matters of life. When we say that the +earth is round we state a truth which every one is willing to +receive as final. If without denying that the earth was round, one +should criticise the statement on the ground that it was not +necessarily round but might be of some other form, we should +simply smile at this use of language. But when we take a more +general statement and assert that the laws of nature are +inexorable, and that all phenomena, so far as we can show, occur +in obedience to their requirements, we are met with a sort of +criticism with which all of us are familiar, but which I am unable +adequately to describe. No one denies that as a matter of fact, +and as far as his experience extends, these laws do appear to be +inexorable. I have never heard of any one professing, during the +present generation, to describe a natural phenomenon, with the +avowed belief that it was not a product of natural law; yet we +constantly hear the scientific view criticised on the ground that +events MAY occur without being subject to natural law. The word +"may," in this connection, is one to which we can attach no +meaning expressive of a sensuous relation. + +The analogous conflict between the scientific use of language and +the use made by some philosophers is found in connection with the +idea of causation. Fundamentally the word cause is used in +scientific language in the same sense as in the language of common +life. When we discuss with our neighbors the cause of a fit of +illness, of a fire, or of cold weather, not the slightest +ambiguity attaches to the use of the word, because whatever +meaning may be given to it is founded only on an accurate analysis +of the ideas involved in it from daily use. No philosopher objects +to the common meaning of the word, yet we frequently find men of +eminence in the intellectual world who will not tolerate the +scientific man in using the word in this way. In every explanation +which he can give to its use they detect ambiguity. They insist +that in any proper use of the term the idea of power must be +connoted. But what meaning is here attached to the word power, and +how shall we first reduce it to a sensible form, and then apply +its meaning to the operations of nature? Whether this can be done, +I do not inquire. All I maintain is that if we wish to do it, we +must pass without the domain of scientific statement. + +Perhaps the greatest advantage in the use of symbolic and other +mathematical language in scientific investigation is that it +cannot possibly be made to connote anything except what the +speaker means. It adheres to the subject matter of discourse with +a tenacity which no criticism can overcome. In consequence, +whenever a science is reduced to a mathematical form its +conclusions are no longer the subject of philosophical attack. To +secure the same desirable quality in all other scientific language +it is necessary to give it, so far as possible, the same +simplicity of signification which attaches to mathematical +symbols. This is not easy, because we are obliged to use words of +ordinary language, and it is impossible to divest them of whatever +they may connote to ordinary hearers. + +I have thus sought to make it clear that the language of science +corresponds to that of ordinary life, and especially of business +life, in confining its meaning to phenomena. An analogous +statement may be made of the method and objects of scientific +investigation. I think Professor Clifford was very happy in +defining science as organized common-sense. The foundation of its +widest general creations is laid, not in any artificial theories, +but in the natural beliefs and tendencies of the human mind. Its +position against those who deny these generalizations is quite +analogous to that taken by the Scottish school of philosophy +against the scepticism of Hume. + +It may be asked, if the methods and language of science correspond +to those of practical life, why is not the every-day discipline of +that life as good as the discipline of science? The answer is, +that the power of transferring the modes of thought of common life +to subjects of a higher order of generality is a rare faculty +which can be acquired only by scientific discipline. What we want +is that in public affairs men shall reason about questions of +finance, trade, national wealth, legislation, and administration, +with the same consciousness of the practical side that they reason +about their own interests. When this habit is once acquired and +appreciated, the scientific method will naturally be applied to +the study of questions of social policy. When a scientific +interest is taken in such questions, their boundaries will be +extended beyond the utilities immediately involved, and one +important condition of unceasing progress will be complied with. + + + + + +XXI + +THE OUTLOOK FOR THE FLYING-MACHINE + + +Mr. Secretary Langley's trial of his flying-machine, which seems +to have come to an abortive issue for the time, strikes a +sympathetic chord in the constitution of our race. Are we not the +lords of creation? Have we not girdled the earth with wires +through which we speak to our antipodes? Do we not journey from +continent to continent over oceans that no animal can cross, and +with a speed of which our ancestors would never have dreamed? Is +not all the rest of the animal creation so far inferior to us in +every point that the best thing it can do is to become completely +subservient to our needs, dying, if need be, that its flesh may +become a toothsome dish on our tables? And yet here is an +insignificant little bird, from whose mind, if mind it has, all +conceptions of natural law are excluded, applying the rules of +aerodynamics in an application of mechanical force to an end we +have never been able to reach, and this with entire ease and +absence of consciousness that it is doing an extraordinary thing. +Surely our knowledge of natural laws, and that inventive genius +which has enabled us to subordinate all nature to our needs, ought +also to enable us to do anything that the bird can do. Therefore +we must fly. If we cannot yet do it, it is only because we have +not got to the bottom of the subject. Our successors of the not +distant future will surely succeed. + +This is at first sight a very natural and plausible view of the +case. And yet there are a number of circumstances of which we +should take account before attempting a confident forecast. Our +hope for the future is based on what we have done in the past. But +when we draw conclusions from past successes we should not lose +sight of the conditions on which success has depended. There is no +advantage which has not its attendant drawbacks; no strength which +has not its concomitant weakness. Wealth has its trials and health +its dangers. We must expect our great superiority to the bird to +be associated with conditions which would give it an advantage at +some point. A little study will make these conditions clear. + +We may look on the bird as a sort of flying-machine complete in +itself, of which a brain and nervous system are fundamentally +necessary parts. No such machine can navigate the air unless +guided by something having life. Apart from this, it could be of +little use to us unless it carried human beings on its wings. We +thus meet with a difficulty at the first step--we cannot give a +brain and nervous system to our machine. These necessary adjuncts +must be supplied by a man, who is no part of the machine, but +something carried by it. The bird is a complete machine in itself. +Our aerial ship must be machine plus man. Now, a man is, I +believe, heavier than any bird that flies. The limit which the +rarity of the air places upon its power of supporting wings, taken +in connection with the combined weight of a man and a machine, +make a drawback which we should not too hastily assume our ability +to overcome. The example of the bird does not prove that man can +fly. The hundred and fifty pounds of dead weight which the manager +of the machine must add to it over and above that necessary in the +bird may well prove an insurmountable obstacle to success. + +I need hardly remark that the advantage possessed by the bird has +its attendant drawbacks when we consider other movements than +flying. Its wings are simply one pair of its legs, and the human +race could not afford to abandon its arms for the most effective +wings that nature or art could supply. + +Another point to be considered is that the bird operates by the +application of a kind of force which is peculiar to the animal +creation, and no approach to which has ever been made in any +mechanism. This force is that which gives rise to muscular action, +of which the necessary condition is the direct action of a nervous +system. We cannot have muscles or nerves for our flying-machine. +We have to replace them by such crude and clumsy adjuncts as +steam-engines and electric batteries. It may certainly seem +singular if man is never to discover any combination of substances +which, under the influence of some such agency as an electric +current, shall expand and contract like a muscle. But, if he is +ever to do so, the time is still in the future. We do not see the +dawn of the age in which such a result will be brought forth. + +Another consideration of a general character may be introduced. As +a rule it is the unexpected that happens in invention as well as +discovery. There are many problems which have fascinated mankind +ever since civilization began which we have made little or no +advance in solving. The only satisfaction we can feel in our +treatment of the great geometrical problems of antiquity is that +we have shown their solution to be impossible. The mathematician +of to-day admits that he can neither square the circle, duplicate +the cube or trisect the angle. May not our mechanicians, in like +manner, be ultimately forced to admit that aerial flight is one of +that great class of problems with which man can never cope, and +give up all attempts to grapple with it? + +[Illustration with caption: PROFESSOR LANGLEY'S AIR-SHIP] + +The fact is that invention and discovery have, notwithstanding +their seemingly wide extent, gone on in rather narrower lines than +is commonly supposed. If, a hundred years ago, the most sagacious +of mortals had been told that before the nineteenth century closed +the face of the earth would be changed, time and space almost +annihilated, and communication between continents made more rapid +and easy than it was between cities in his time; and if he had +been asked to exercise his wildest imagination in depicting what +might come--the airship and the flying-machine would probably have +had a prominent place in his scheme, but neither the steamship, +the railway, the telegraph, nor the telephone would have been +there. Probably not a single new agency which he could have +imagined would have been one that has come to pass. + +It is quite clear to me that success must await progress of a +different kind from that which the inventors of flying-machines +are aiming at. We want a great discovery, not a great invention. +It is an unfortunate fact that we do not always appreciate the +distinction between progress in scientific discovery and ingenious +application of discovery to the wants of civilization. The name of +Marconi is familiar to every ear; the names of Maxwell and Herz, +who made the discoveries which rendered wireless telegraphy +possible, are rarely recalled. Modern progress is the result of +two factors: Discoveries of the laws of nature and of actions or +possibilities in nature, and the application of such discoveries +to practical purposes. The first is the work of the scientific +investigator, the second that of the inventor. + +In view of the scientific discoveries of the past ten years, +which, after bringing about results that would have seemed +chimerical if predicted, leading on to the extraction of a +substance which seems to set the laws and limits of nature at +defiance by radiating a flood of heat, even when cooled to the +lowest point that science can reach--a substance, a few specks of +which contain power enough to start a railway train, and embody +perpetual motion itself, almost--he would be a bold prophet who +would set any limit to possible discoveries in the realm of +nature. We are binding the universe together by agencies which +pass from sun to planet and from star to star. We are determined +to find out all we can about the mysterious ethereal medium +supposed to fill all space, and which conveys light and heat from +one heavenly body to another, but which yet evades all direct +investigation. We are peering into the law of gravitation itself +with the full hope of discovering something in its origin which +may enable us to evade its action. From time to time philosophers +fancy the road open to success, yet nothing that can be +practically called success has yet been reached or even +approached. When it is reached, when we are able to state exactly +why matter gravitates, then will arise the question how this +hitherto unchangeable force may be controlled and regulated. With +this question answered the problem of the interaction between +ether and matter may be solved. That interaction goes on between +ethers and molecules is shown by the radiation of heat by all +bodies. When the molecules are combined into a mass, this +interaction ceases, so that the lightest objects fly through the +ether without resistance. Why is this? Why does ether act on the +molecule and not the mass? When we can produce the latter, and +when the mutual action can be controlled, then may gravitation be +overcome and then may men build, not merely airships, but ships +which shall fly above the air, and transport their passengers from +continent to continent with the speed of the celestial motions. + +The first question suggested to the reader by these considerations +is whether any such result is possible; whether it is within the +power of man to discover the nature of luminiferous ether and the +cause of gravitation. To this the profoundest philosopher can only +answer, "I do not know." Quite possibly the gates at which he is +beating are, in the very nature of things, incapable of being +opened. It may be that the mind of man is incapable of grasping +the secrets within them. The question has even occurred to me +whether, if a being of such supernatural power as to understand +the operations going on in a molecule of matter or in a current of +electricity as we understand the operations of a steam-engine +should essay to explain them to us, he would meet with any more +success than we should in explaining to a fish the engines of a +ship which so rudely invades its domain. As was remarked by +William K. Clifford, perhaps the clearest spirit that has ever +studied such problems, it is possible that the laws of geometry +for spaces infinitely small may be so different from those of +larger spaces that we must necessarily be unable to conceive them. + +Still, considering mere possibilities, it is not impossible that +the twentieth century may be destined to make known natural forces +which will enable us to fly from continent to continent with a +speed far exceeding that of the bird. + +But when we inquire whether aerial flight is possible in the +present state of our knowledge, whether, with such materials as we +possess, a combination of steel, cloth, and wire can be made +which, moved by the power of electricity or steam, shall form a +successful flying-machine, the outlook may be altogether +different. To judge it sanely, let us bear in mind the +difficulties which are encountered in any flying-machine. The +basic principle on which any such machine must be constructed is +that of the aeroplane. This, by itself, would be the simplest of +all flyers, and therefore the best if it could be put into +operation. The principle involved may be readily comprehended by +the accompanying figure. A M is the section of a flat plane +surface, say a thin sheet of metal or a cloth supported by wires. +It moves through the air, the latter being represented by the +horizontal rows of dots. The direction of the motion is that of +the horizontal line A P. The aeroplane has a slight inclination +measured by the proportion between the perpendicular M P and the +length A P. We may raise the edge M up or lower it at pleasure. +Now the interesting point, and that on which the hopes of +inventors are based, is that if we give the plane any given +inclination, even one so small that the perpendicular M P is only +two or three per cent of the length A M, we can also calculate a +certain speed of motion through the air which, if given to the +plane, will enable it to bear any required weight. A plane ten +feet square, for example, would not need any great inclination, +nor would it require a speed higher than a few hundred feet a +second to bear a man. What is of yet more importance, the higher +the speed the less the inclination required, and, if we leave out +of consideration the friction of the air and the resistance +arising from any object which the machine may carry, the less the +horse-power expended in driving the plane. + +[Illustration] + +Maxim exemplified this by experiment several years ago. He found +that, with a small inclination, he could readily give his +aeroplane, when it slid forward upon ways, such a speed that it +would rise from the ways of itself. The whole problem of the +successful flying-machine is, therefore, that of arranging an +aeroplane that shall move through the air with the requisite +speed. + +The practical difficulties in the way of realizing the movement of +such an object are obvious. The aeroplane must have its +propellers. These must be driven by an engine with a source of +power. Weight is an essential quality of every engine. The +propellers must be made of metal, which has its weakness, and +which is liable to give way when its speed attains a certain +limit. And, granting complete success, imagine the proud possessor +of the aeroplane darting through the air at a speed of several +hundred feet per second! It is the speed alone that sustains him. +How is he ever going to stop? Once he slackens his speed, down he +begins to fall. He may, indeed, increase the inclination of his +aeroplane. Then he increases the resistance to the sustaining +force. Once he stops he falls a dead mass. How shall he reach the +ground without destroying his delicate machinery? I do not think +the most imaginative inventor has yet even put upon paper a +demonstratively successful way of meeting this difficulty. The +only ray of hope is afforded by the bird. The latter does succeed +in stopping and reaching the ground safely after its flight. But +we have already mentioned the great advantages which the bird +possesses in the power of applying force to its wings, which, in +its case, form the aeroplanes. But we have already seen that there +is no mechanical combination, and no way of applying force, which +will give to the aeroplanes the flexibility and rapidity of +movement belonging to the wings of a bird. With all the +improvements that the genius of man has made in the steamship, the +greatest and best ever constructed is liable now and then to meet +with accident. When this happens she simply floats on the water +until the damage is repaired, or help reaches her. Unless we are +to suppose for the flying-machine, in addition to everything else, +an immunity from accident which no human experience leads us to +believe possible, it would be liable to derangements of machinery, +any one of which would be necessarily fatal. If an engine were +necessary not only to propel a ship, but also to make her float-- +if, on the occasion of any accident she immediately went to the +bottom with all on board--there would not, at the present day, be +any such thing as steam navigation. That this difficulty is +insurmountable would seem to be a very fair deduction, not only +from the failure of all attempts to surmount it, but from the fact +that Maxim has never, so far as we are aware, followed up his +seemingly successful experiment. + +There is, indeed, a way of attacking it which may, at first sight, +seem plausible. In order that the aeroplane may have its full +sustaining power, there is no need that its motion be continuously +forward. A nearly horizontal surface, swinging around in a circle, +on a vertical axis, like the wings of a windmill moving +horizontally, will fulfil all the conditions. In fact, we have a +machine on this simple principle in the familiar toy which, set +rapidly whirling, rises in the air. Why more attempts have not +been made to apply this system, with two sets of sails whirling in +opposite directions, I do not know. Were there any possibility of +making a flying-machine, it would seem that we should look in this +direction. + +The difficulties which I have pointed out are only preliminary +ones, patent on the surface. A more fundamental one still, which +the writer feels may prove insurmountable, is based on a law of +nature which we are bound to accept. It is that when we increase +the size of any flying-machine without changing its model we +increase the weight in proportion to the cube of the linear +dimensions, while the effective supporting power of the air +increases only as the square of those dimensions. To illustrate +the principle let us make two flying-machines exactly alike, only +make one on double the scale of the other in all its dimensions. +We all know that the volume and therefore the weight of two +similar bodies are proportional to the cubes of their dimensions. +The cube of two is eight. Hence the large machine will have eight +times the weight of the other. But surfaces are as the squares of +the dimensions. The square of two is four. The heavier machine +will therefore expose only four times the wing surface to the air, +and so will have a distinct disadvantage in the ratio of +efficiency to weight. + +Mechanical principles show that the steam pressures which the +engines would bear would be the same, and that the larger engine, +though it would have more than four times the horse-power of the +other, would have less than eight times. The larger of the two +machines would therefore be at a disadvantage, which could be +overcome only by reducing the thickness of its parts, especially +of its wings, to that of the other machine. Then we should lose in +strength. It follows that the smaller the machine the greater its +advantage, and the smallest possible flying-machine will be the +first one to be successful. + +We see the principle of the cube exemplified in the animal +kingdom. The agile flea, the nimble ant, the swift-footed +greyhound, and the unwieldy elephant form a series of which the +next term would be an animal tottering under its own weight, if +able to stand or move at all. The kingdom of flying animals shows +a similar gradation. The most numerous fliers are little insects, +and the rising series stops with the condor, which, though having +much less weight than a man, is said to fly with difficulty when +gorged with food. + +Now, suppose that an inventor succeeds, as well he may, in making +a machine which would go into a watch-case, yet complete in all +its parts, able to fly around the room. It may carry a button, but +nothing heavier. Elated by his success, he makes one on the same +model twice as large in every dimension. The parts of the first, +which are one inch in length, he increases to two inches. Every +part is twice as long, twice as broad, and twice as thick. The +result is that his machine is eight times as heavy as before. But +the sustaining surface is only four times as great. As compared +with the smaller machine, its ratio of effectiveness is reduced to +one-half. It may carry two or three buttons, but will not carry +over four, because the total weight, machine plus buttons, can +only be quadrupled, and if he more than quadruples the weight of +the machine, he must less than quadruple that of the load. How +many such enlargements must he make before his machine will cease +to sustain itself, before it will fall as an inert mass when we +seek to make it fly through the air? Is there any size at which it +will be able to support a human being? We may well hesitate before +we answer this question in the affirmative. + +Dr. Graham Bell, with a cheery optimism very pleasant to +contemplate, has pointed out that the law I have just cited may be +evaded by not making a larger machine on the same model, but +changing the latter in a way tantamount to increasing the number +of small machines. This is quite true, and I wish it understood +that, in laying down the law I have cited, I limit it to two +machines of different sizes on the same model throughout. Quite +likely the most effective flying-machine would be one carried by a +vast number of little birds. The veracious chronicler who escaped +from a cloud of mosquitoes by crawling into an immense metal pot +and then amused himself by clinching the antennae of the insects +which bored through the pot until, to his horror, they became so +numerous as to fly off with the covering, was more scientific than +he supposed. Yes, a sufficient number of humming-birds, if we +could combine their forces, would carry an aerial excursion party +of human beings through the air. If the watch-maker can make a +machine which will fly through the room with a button, then, by +combining ten thousand such machines he may be able to carry a +man. But how shall the combined forces be applied? + +The difficulties I have pointed out apply only to the flying- +machine properly so-called, and not to the dirigible balloon or +airship. It is of interest to notice that the law is reversed in +the case of a body which is not supported by the resistance of a +fluid in which it is immersed, but floats in it, the ship or +balloon, for example. When we double the linear dimensions of a +steamship in all its parts, we increase not only her weight but +her floating power, her carrying capacity, and her engine capacity +eightfold. But the resistance which she meets with when passing +through the water at a given speed is only multiplied four times. +Hence, the larger we build the steamship the more economical the +application of the power necessary to drive it at a given speed. +It is this law which has brought the great increase in the size of +ocean steamers in recent times. The proportionately diminishing +resistance which, in the flying-machine, represents the floating +power is, in the ship, something to be overcome. Thus there is a +complete reversal of the law in its practical application to the +two cases. + +The balloon is in the same class with the ship. Practical +difficulties aside, the larger it is built the more effective it +will be, and the more advantageous will be the ratio of the power +which is necessary to drive it to the resistance to be overcome. + +If, therefore, we are ever to have aerial navigation with our +present knowledge of natural capabilities, it is to the airship +floating in the air, rather than the flying-machine resting on the +air, to which we are to look. In the light of the law which I have +laid down, the subject, while not at all promising, seems worthy +of more attention than it has received. It is not at all unlikely +that if a skilful and experienced naval constructor, aided by an +able corps of assistants, should design an airship of a diameter +of not less than two hundred feet, and a length at least four or +five times as great, constructed, possibly, of a textile substance +impervious to gas and borne by a light framework, but, more +likely, of exceedingly thin plates of steel carried by a frame +fitted to secure the greatest combination of strength and +lightness, he might find the result to be, ideally at least, a +ship which would be driven through the air by a steam-engine with +a velocity far exceeding that of the fleetest Atlantic liner. Then +would come the practical problem of realizing the ship by +overcoming the mechanical difficulties involved in the +construction of such a huge and light framework. I would not be at +all surprised if the result of the exact calculation necessary to +determine the question should lead to an affirmative conclusion, +but I am quite unable to judge whether steel could be rolled into +parts of the size and form required in the mechanism. + +In judging of the possibility of commercial success the cheapness +of modern transportation is an element in the case that should not +be overlooked. I believe the principal part of the resistance +which a limited express train meets is the resistance of the air. +This would be as great for an airship as for a train. An important +fraction of the cost of transporting goods from Chicago to London +is that of getting them into vehicles, whether cars or ships, and +getting them out again. The cost of sending a pair of shoes from a +shop in New York to the residence of the wearer is, if I mistake +not, much greater than the mere cost of transporting them across +the Atlantic. Even if a dirigible balloon should cross the +Atlantic, it does not follow that it could compete with the +steamship in carrying passengers and freight. + +I may, in conclusion, caution the reader on one point. I should be +very sorry if my suggestion of the advantage of the huge airship +leads to the subject being taken up by any other than skilful +engineers or constructors, able to grapple with all problems +relating to the strength and resistance of materials. As a single +example of what is to be avoided I may mention the project, which +sometimes has been mooted, of making a balloon by pumping the air +from a very thin, hollow receptacle. Such a project is as futile +as can well be imagined; no known substance would begin to resist +the necessary pressure. Our aerial ship must be filled with some +substance lighter than air. Whether heated air would answer the +purpose, or whether we should have to use a gas, is a question for +the designer. + +To return to our main theme, all should admit that if any hope for +the flying-machine can be entertained, it must be based more on +general faith in what mankind is going to do than upon either +reasoning or experience. We have solved the problem of talking +between two widely separated cities, and of telegraphing from +continent to continent and island to island under all the oceans-- +therefore we shall solve the problem of flying. But, as I have +already intimated, there is another great fact of progress which +should limit this hope. As an almost universal rule we have never +solved a problem at which our predecessors have worked in vain, +unless through the discovery of some agency of which they have had +no conception. The demonstration that no possible combination of +known substances, known forms of machinery, and known forms of +force can be united in a practicable machine by which men shall +fly long distances through the air, seems to the writer as +complete as it is possible for the demonstration of any physical +fact to be. But let us discover a substance a hundred times as +strong as steel, and with that some form of force hitherto +unsuspected which will enable us to utilize this strength, or let +us discover some way of reversing the law of gravitation so that +matter may be repelled by the earth instead of attracted--then we +may have a flying-machine. But we have every reason to believe +that mere ingenious contrivances with our present means and forms +of force will be as vain in the future as they have been in the +past. + + + +End of Project Gutenberg's Side-Lights On Astronomy, by Simon Newcomb + diff --git a/old/slstr10.zip b/old/slstr10.zip Binary files differnew file mode 100644 index 0000000..6caef2c --- /dev/null +++ b/old/slstr10.zip |